Mathematika, ISSN 0025-5793, 01/2020, Volume 66, Issue 1, pp. 144 - 160

In signal processing the Rudin–Shapiro polynomials have good autocorrelation properties and their values on the unit circle are small. Binary sequences with...

26C10 (primary) | 11C08 | 30C15 (secondary) | 41A17

26C10 (primary) | 11C08 | 30C15 (secondary) | 41A17

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 9/2013, Volume 77, Issue 1, pp. 123 - 148

As applications of atomic decomposition results of Hardy spaces with variable exponents, we shall prove the boundedness of commutators and the fractional...

42B35 | atomic decomposition | Analysis | fractional integral operators | 26A33 | Hardy spaces | Primary 41A17 | Mathematics | Secondary 42B25 | MATHEMATICS

42B35 | atomic decomposition | Analysis | fractional integral operators | 26A33 | Hardy spaces | Primary 41A17 | Mathematics | Secondary 42B25 | MATHEMATICS

Journal Article

Constructive Approximation, ISSN 0176-4276, 12/2016, Volume 44, Issue 3, pp. 327 - 338

Let $${\mathbf{x}}=(x_1,\dots ,x_d) \in [-1,1]^d$$ x = ( x 1 , ⋯ , x d ) ∈ [ - 1 , 1 ] d be linearly independent over $$\mathbb {Z}$$ Z , and set...

Hausdorff dimension | Numerical Analysis | Analysis | Secondary 11J13 | Primary 41A17 | Mathematics | Polynomial inequalities | Liouville vectors | 30D15 | 41A17 | Bernstein–Walsh inequalities | MATHEMATICS | Bernstein-Walsh inequalities

Hausdorff dimension | Numerical Analysis | Analysis | Secondary 11J13 | Primary 41A17 | Mathematics | Polynomial inequalities | Liouville vectors | 30D15 | 41A17 | Bernstein–Walsh inequalities | MATHEMATICS | Bernstein-Walsh inequalities

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 12/2007, Volume 257, Issue 4, pp. 871 - 905

The aim of this paper is to define the Besov–Morrey spaces and the Triebel– Lizorkin–Morrey spaces and to present a decomposition of functions belonging to...

Decomposition of functions | Besov | Mathematics, general | Triebel–Lizorkin space | Mathematics | Primary 42B35 | Morrey space | Secondary 41A17 | Triebel-Lizorkin space | MATHEMATICS | EQUATION | decomposition of functions

Decomposition of functions | Besov | Mathematics, general | Triebel–Lizorkin space | Mathematics | Primary 42B35 | Morrey space | Secondary 41A17 | Triebel-Lizorkin space | MATHEMATICS | EQUATION | decomposition of functions

Journal Article

Constructive Approximation, ISSN 0176-4276, 12/2019, Volume 50, Issue 3, pp. 543 - 577

We prove invariance theorems for general inequalities of different metrics and apply them to limit relations between the sharp constants in the multivariate...

Entire functions of exponential type | 41A63 | Secondary 26D10 | Numerical Analysis | Analysis | Sharp constants | Primary 41A17 | Mathematics | Algebraic polynomials | Weighted spaces | Multivariate Markov–Bernstein–Nikolskii type inequality | Mathematics - Classical Analysis and ODEs

Entire functions of exponential type | 41A63 | Secondary 26D10 | Numerical Analysis | Analysis | Sharp constants | Primary 41A17 | Mathematics | Algebraic polynomials | Weighted spaces | Multivariate Markov–Bernstein–Nikolskii type inequality | Mathematics - Classical Analysis and ODEs

Journal Article

6.
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Generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on domains

Mathematische Nachrichten, ISSN 0025-584X, 10/2019, Volume 292, Issue 10, pp. 2212 - 2251

In this paper, we consider a non‐smooth atomic decomposition by using a smooth atomic decomposition. Applying the non‐smooth atomic decomposition, a local...

Primary: 42B35; Secondary: 41A17 | Triebel–Lizorkin space | non‐smooth atomic decomposition | trace operator | Besov space | Morrey space | TRACE | MATHEMATICS | DECOMPOSITIONS | Secondary | Triebel-Lizorkin space | Primary | non-smooth atomic decomposition | OPERATORS

Primary: 42B35; Secondary: 41A17 | Triebel–Lizorkin space | non‐smooth atomic decomposition | trace operator | Besov space | Morrey space | TRACE | MATHEMATICS | DECOMPOSITIONS | Secondary | Triebel-Lizorkin space | Primary | non-smooth atomic decomposition | OPERATORS

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 04/2018, Volume 21, Issue 2, pp. 399 - 422

The objective of this paper is to construct fractional wavelet frames in (ℝ). A necessary condition and four sufficient conditions for fractional wavelet...

fractional wavelet transform | fractional wavelet | Secondary 42C15, 41A17, 46F12, 26A33 | Primary 42C40 | fractional Fourier transform | wavelet frame | Frames | Wavelet analysis | Fourier transforms | Inequalities

fractional wavelet transform | fractional wavelet | Secondary 42C15, 41A17, 46F12, 26A33 | Primary 42C40 | fractional Fourier transform | wavelet frame | Frames | Wavelet analysis | Fourier transforms | Inequalities

Journal Article

Numerische Mathematik, ISSN 0029-599X, 11/2018, Volume 140, Issue 3, pp. 755 - 790

The Euler–Maclaurin (EM) summation formula is used in many theoretical studies and numerical calculations. It approximates the sum $${\sum \nolimits...

68Q17 (Secondary) | Theoretical, Mathematical and Computational Physics | 41A80 | Mathematics | 41A60 | 41A35 (Primary) | 41A55 | 65D30 | Mathematical Methods in Physics | 41A35 | 41A25 | 41A58 | Numerical Analysis | 65D10 | 65D32 | Mathematical and Computational Engineering | 41A10 | Mathematics, general | 26A06 | 26A36 | Numerical and Computational Physics, Simulation | 41A17 | MATHEMATICS, APPLIED | BERNOULLI NUMBERS

68Q17 (Secondary) | Theoretical, Mathematical and Computational Physics | 41A80 | Mathematics | 41A60 | 41A35 (Primary) | 41A55 | 65D30 | Mathematical Methods in Physics | 41A35 | 41A25 | 41A58 | Numerical Analysis | 65D10 | 65D32 | Mathematical and Computational Engineering | 41A10 | Mathematics, general | 26A06 | 26A36 | Numerical and Computational Physics, Simulation | 41A17 | MATHEMATICS, APPLIED | BERNOULLI NUMBERS

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 9/2019, Volume 29, Issue 4, pp. 1 - 12

In this paper we prove that the Turán inequality in quaternionic setting holds for all polynomials of degree $$n\le 2$$ n≤2 and for some particular subclasses...

Mathematical Methods in Physics | Quaternionic polynomials | Theoretical, Mathematical and Computational Physics | Applications of Mathematics | Physics, general | Physics | Primary: 30G35 | Turán’s inequality | Secondary: 41A17 | Turan's inequality | REGULAR FUNCTIONS | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Computer science | Equality

Mathematical Methods in Physics | Quaternionic polynomials | Theoretical, Mathematical and Computational Physics | Applications of Mathematics | Physics, general | Physics | Primary: 30G35 | Turán’s inequality | Secondary: 41A17 | Turan's inequality | REGULAR FUNCTIONS | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Computer science | Equality

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 9/2019, Volume 13, Issue 6, pp. 2687 - 2706

In this paper we extend Luzin inequality for functions defined by the Cauchy-Leray-Fantappiè integral on the complement of a convex domain in $$\mathbb {C}^n$$...

Singular integral operator | Operator Theory | Primary 32A55 | Analysis | Mathematics, general | Mathematics | Area inequality | Secondary 41A17 | Cauchy-Leray-Fantappiè integral | MATHEMATICS | MATHEMATICS, APPLIED | Cauchy-Leray-Fantappie integral | DOMAINS | Numerical analysis | Equality

Singular integral operator | Operator Theory | Primary 32A55 | Analysis | Mathematics, general | Mathematics | Area inequality | Secondary 41A17 | Cauchy-Leray-Fantappiè integral | MATHEMATICS | MATHEMATICS, APPLIED | Cauchy-Leray-Fantappie integral | DOMAINS | Numerical analysis | Equality

Journal Article

Revista Matemática Complutense, ISSN 1139-1138, 5/2016, Volume 29, Issue 2, pp. 341 - 404

This paper is concerned with the boundedness of trace and extension operators for Besov spaces and Triebel–Lizorkin spaces with variable exponents on the upper...

Triebel-Lizorkin space | Mathematics | Topology | Variable exponents | Quarkonial decomposition | Besov space | Trace operator | Geometry | Algebra | Extension operator | Analysis | Mathematics, general | Applications of Mathematics | Primary 42B35 | Secondary 41A17 | MATHEMATICS, APPLIED | INTEGRABILITY | 2-MICROLOCAL BESOV | SMOOTHNESS | DECOMPOSITION | MATHEMATICS | LEBESGUE | MORREY SPACES

Triebel-Lizorkin space | Mathematics | Topology | Variable exponents | Quarkonial decomposition | Besov space | Trace operator | Geometry | Algebra | Extension operator | Analysis | Mathematics, general | Applications of Mathematics | Primary 42B35 | Secondary 41A17 | MATHEMATICS, APPLIED | INTEGRABILITY | 2-MICROLOCAL BESOV | SMOOTHNESS | DECOMPOSITION | MATHEMATICS | LEBESGUE | MORREY SPACES

Journal Article

Constructive Approximation, ISSN 0176-4276, 4/2017, Volume 45, Issue 2, pp. 143 - 191

Nonlinear approximation from regular piecewise polynomials (splines) supported on rings in $$\mathbb {R}^2$$ R 2 is studied. By definition, a ring is a set in...

Multivariate approximation | Mathematics | Jackson estimate | Besov spaces | Spline approximation | Bernstein estimate | 41A25 | Numerical Analysis | Analysis | 41A27 | Nonlinear approximation | Secondary 41A17 | Primary 41A15 | MATHEMATICS | BESOV-SPACES | Naturvetenskap | Natural Sciences | Matematik

Multivariate approximation | Mathematics | Jackson estimate | Besov spaces | Spline approximation | Bernstein estimate | 41A25 | Numerical Analysis | Analysis | 41A27 | Nonlinear approximation | Secondary 41A17 | Primary 41A15 | MATHEMATICS | BESOV-SPACES | Naturvetenskap | Natural Sciences | Matematik

Journal Article

Results in Mathematics, ISSN 1422-6383, 3/2018, Volume 73, Issue 1, pp. 1 - 21

As is known, if $$f\in C^2[0,1]$$ f∈C2[0,1] , then, for the Bernstein operator $$B_n$$ Bn , there holds $$\begin{aligned} \lim _{n\rightarrow \infty } n(B_n...

converse estimate | Voronovskaya inequality | K -functional | Mathematics, general | Mathematics | modulus of smoothness | Primary 41A25 | Bernstein polynomials | direct estimate | Secondary 41A10, 41A17, 41A27, 41A35, 41A40 | K-functional | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | THEOREM

converse estimate | Voronovskaya inequality | K -functional | Mathematics, general | Mathematics | modulus of smoothness | Primary 41A25 | Bernstein polynomials | direct estimate | Secondary 41A10, 41A17, 41A27, 41A35, 41A40 | K-functional | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | APPROXIMATION | THEOREM

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 10/2017, Volume 11, Issue 7, pp. 1569 - 1586

In this work, we investigate the order of growth of the modulus of an arbitrary algebraic polynomials in the weighted Lebesgue space, where the contour and the...

30C10 | Operator Theory | Primary 30A10 | Conformal mapping | Analysis | Mathematics, general | Mathematics | Algebraic polynomials | Orthonormal polynomials | Quasicircle | Secondary 41A17 | MATHEMATICS | MATHEMATICS, APPLIED | ORTHOGONAL POLYNOMIALS | COMPLEX-PLANE | BOUNDARY

30C10 | Operator Theory | Primary 30A10 | Conformal mapping | Analysis | Mathematics, general | Mathematics | Algebraic polynomials | Orthonormal polynomials | Quasicircle | Secondary 41A17 | MATHEMATICS | MATHEMATICS, APPLIED | ORTHOGONAL POLYNOMIALS | COMPLEX-PLANE | BOUNDARY

Journal Article

Positivity, ISSN 1385-1292, 9/2017, Volume 21, Issue 3, pp. 1223 - 1252

We develop and apply a decomposition theory for generic local Morrey-type spaces. Our result is nonsmooth decomposition, which follows from the fact that local...

Molecular decomposition | 42B35 (Secondary) | Mathematics | Morrey-type spaces | 42B20 (Primary) | Maximal operators | Operator Theory | Fourier Analysis | 42B25 | Potential Theory | Calculus of Variations and Optimal Control; Optimization | Econometrics | 41A17 | Atomic decomposition | MATHEMATICS | FRACTIONAL MAXIMAL OPERATOR | SUFFICIENT CONDITIONS | EQUATIONS | BOUNDEDNESS | WEIGHTED HARDY | Information science | Marijuana | Decomposition

Molecular decomposition | 42B35 (Secondary) | Mathematics | Morrey-type spaces | 42B20 (Primary) | Maximal operators | Operator Theory | Fourier Analysis | 42B25 | Potential Theory | Calculus of Variations and Optimal Control; Optimization | Econometrics | 41A17 | Atomic decomposition | MATHEMATICS | FRACTIONAL MAXIMAL OPERATOR | SUFFICIENT CONDITIONS | EQUATIONS | BOUNDEDNESS | WEIGHTED HARDY | Information science | Marijuana | Decomposition

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 10/2016, Volume 150, Issue 1, pp. 99 - 120

Let W be a k-concave weight on an open convex set V in $${{\mathbb R}^m}$$ R m , $${k \in [0, \infty]}$$ k ∈ [ 0 , ∞ ] , and let $${\mu_W}$$ μ W be the...

log-concave measure | (1/ d )-concave measure | Mathematics, general | Mathematics | polynomial inequality of different metrics | primary 41A17 | secondary 26D05 | multivariate polynomial | MATHEMATICS | CONVEX-BODIES | Q NORM INEQUALITIES | MEASURABLE SETS | (1/d)-concave measure

log-concave measure | (1/ d )-concave measure | Mathematics, general | Mathematics | polynomial inequality of different metrics | primary 41A17 | secondary 26D05 | multivariate polynomial | MATHEMATICS | CONVEX-BODIES | Q NORM INEQUALITIES | MEASURABLE SETS | (1/d)-concave measure

Journal Article

17.
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Multivariate polynomial inequalities of different Lp,W(V) -metrics with k-concave weights

Acta Mathematica Hungarica, ISSN 0236-5294, 10/2016, Volume 150, Issue 1, pp. 99 - 120

Journal Article

Journal of Fourier Analysis and Applications, ISSN 1069-5869, 10/2014, Volume 20, Issue 5, pp. 1020 - 1049

We establish inequalities of Ulyanov-type for moduli of smoothness relating the source Lorentz–Zygmund space $$\, L^{p,r}(\log L)^{\alpha -\gamma },\, \gamma...

Signal, Image and Speech Processing | Mathematics | Lorentz–Zygmund spaces | Moduli of smoothness | K$$ K -functionals | Abstract Harmonic Analysis | Mathematical Methods in Physics | Fourier Analysis | 46E35 | 46E30 | Approximations and Expansions | Primary 41A17 | Secondary 42B15 | Partial Differential Equations | K-functionals | MATHEMATICS, APPLIED | REITERATION | APPROXIMATION | SMOOTHNESS | Lorentz-Zygmund spaces | MODULI | BANACH-SPACES | THEOREMS | EMBEDDINGS | REAL INTERPOLATION | DERIVATIVES | Analysis | Algebra

Signal, Image and Speech Processing | Mathematics | Lorentz–Zygmund spaces | Moduli of smoothness | K$$ K -functionals | Abstract Harmonic Analysis | Mathematical Methods in Physics | Fourier Analysis | 46E35 | 46E30 | Approximations and Expansions | Primary 41A17 | Secondary 42B15 | Partial Differential Equations | K-functionals | MATHEMATICS, APPLIED | REITERATION | APPROXIMATION | SMOOTHNESS | Lorentz-Zygmund spaces | MODULI | BANACH-SPACES | THEOREMS | EMBEDDINGS | REAL INTERPOLATION | DERIVATIVES | Analysis | Algebra

Journal Article

International Journal of Analysis, ISSN 2314-498X, 01/2015, Volume 2015

We study [superscript]Lp[/superscript] boundedness of the de la Vallee Poussin means [subscript]vn[/subscript] (f) for exponential weight w(x)=exp(-Q(x)) on...

Mathematical analysis | Polynomials | Approximation

Mathematical analysis | Polynomials | Approximation

Journal Article

Results in Mathematics, ISSN 1422-6383, 9/2014, Volume 66, Issue 1, pp. 21 - 41

The paper presents upper estimates of the error of weighted and unweighted simultaneous approximation by the Bernstein operators and their iterated Boolean...

iterates | Mathematics | modulus of smoothness | Bernstein polynomials | Boolean sums | 41A35 | upper error estimate | 41A25 | 41A36 | simultaneous approximation | Secondary 41A10 | K -functional | Mathematics, general | Primary 41A28 | 41A17 | K-functional | MATHEMATICS | MATHEMATICS, APPLIED | K-FUNCTIONALS | THEOREMS

iterates | Mathematics | modulus of smoothness | Bernstein polynomials | Boolean sums | 41A35 | upper error estimate | 41A25 | 41A36 | simultaneous approximation | Secondary 41A10 | K -functional | Mathematics, general | Primary 41A28 | 41A17 | K-functional | MATHEMATICS | MATHEMATICS, APPLIED | K-FUNCTIONALS | THEOREMS

Journal Article

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