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Journal of Fourier Analysis and Applications, ISSN 1069-5869, 12/2018, Volume 24, Issue 6, pp. 1539 - 1553
... 1 David Edmunds 1 · Amiran Gogatishvili 2 · Tengiz Kopaliani 3 Received: 15 December 2016 / Revised: 4 October 2017 / Published online: 26 October 2017... 
Hardy–Littlewood maximal function | Mathematics | Abstract Harmonic Analysis | Mathematical Methods in Physics | Fourier Analysis | Signal,Image and Speech Processing | 42A20 | Banach function space | 46E30 | Approximations and Expansions | a.e. divergent Fourier series | Partial Differential Equations | Variable Lebesgue spaces
Journal Article
Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2015, Volume 67, Issue 2, pp. 581 - 593
In this paper maximal commutators and commutators of maximal functions with functions of bounded mean oscillation are investigated. New pointwise estimates for... 
BMO | Commutator | Maximal operator | maximal operator | commutator | MATHEMATICS | SPACES | WEIGHTED NORM INEQUALITIES | SINGULAR INTEGRAL-OPERATORS | MEAN OSCILLATION
Journal Article
Forum mathematicum, ISSN 1435-5337, 2011, Volume 25, Issue 4, pp. - - -
On a metric measure space satisfying the doubling property, we establish several optimal characterizations of Besov and Triebel–Lizorkin spaces, including a... 
Triebel–Lizorkin space | Hajłasz–Triebel–Lizorkin space | Hajłasz–Besov space | sharp maximal function | Besov space | metric measure space | MATHEMATICS | MATHEMATICS, APPLIED | SOBOLEV SPACES | MAXIMAL FUNCTIONS | Triebel-Lizorkin space | INEQUALITY | Hajlasz-Besov space | EXTENSION | Hajlasz-Triebel-Lizorkin space
Journal Article
Positivity, ISSN 1385-1292, 6/2014, Volume 18, Issue 2, pp. 319 - 345
...Positivity (2014) 18:319–345 DOI 10.1007/s11117-013-0246-4 Positivity The rearrangement-invariant space null p,φ Amiran Gogatishvili · Ron Kerman Received: 30... 
Mathematics | Caldéron–Zygmund operator | Hardy operator | Operator Theory | Lorentz Gamma space | Weighted norm inequalities | Fourier Analysis | Potential Theory | Köthe dual space | Calculus of Variations and Optimal Control; Optimization | Primary 46E30 | Secondary 26D10 | Econometrics | Stieltjes transform
Journal Article
Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, ISSN 0308-2105, 10/2016, Volume 146, Issue 5, pp. 905 - 927
... in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal (acaetano@ua.pt) Amiran Gogatishvili Institute of Mathematics... 
compactness | compact embedding | quasi-Banach function space | absolute continuity | Besov space | Lorentz space | MATHEMATICS | MATHEMATICS, APPLIED | LORENTZ SPACES | Function space | Paper | Criteria | Mathematics - Functional Analysis
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2016, Volume 433, Issue 2, pp. 1350 - 1368
Let ℓ∈N and p∈(1,∞]. In this article, the authors prove that the sequence {f−Bℓ,2−kf}k∈Z consisting of the differences between f and the ball average Bℓ,2−kf... 
Triebel–Lizorkin space | Difference | Average on ball | Besov space | Calderón reproducing formula | Triebel-Lizorkin space | MATHEMATICS | MATHEMATICS, APPLIED | SOBOLEV SPACES | INEQUALITIES | Calderon reproducing formula
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 2013, Volume 405, Issue 1, pp. 156 - 172
For a quasilinear operator on the semiaxis a reduction theorem is proved on the cones of monotone functions in the Lp−Lq setting for 0 Quasilinear operator | Hardy operator | Lebesgue space | Integral inequality | Monotone functions | Weight | MATHEMATICS, APPLIED | NONINCREASING FUNCTIONS | WEIGHTED HARDY INEQUALITIES | BOUNDEDNESS | MATHEMATICS | CLASSICAL LORENTZ SPACES | EMBEDDINGS | INTEGRAL-OPERATORS
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 12/2019, Volume 69, Issue 6, pp. 1303 - 1328
In this paper the solution of the pointwise multiplier problem between weighted Copson function spaces Cop , ) and weighted Cesàro function spaces Ces , ) is... 
embeddings | iterated Hardy inequalities | Primary 26D10 | weights | Secondary 26D15 | Cesàro and Copson function spaces | MATHEMATICS | Cesaro and Copson function spaces | DUALITY
Journal Article
Mathematical Inequalities and Applications, ISSN 1331-4343, 07/2017, Volume 20, Issue 3, pp. 683 - 728
In this paper reduction and equivalence theorems for the boundedness of the composition of a quasilinear operator T with the Hardy and Copson operators in... 
Quasilinear operators | Weights | Iterated Hardy inequalities | CONES | BOUNDEDNESS | weights | MORREY-TYPE SPACES | MONOTONE-FUNCTIONS | MATHEMATICS | EQUIVALENT CONDITIONS | CLASSICAL LORENTZ SPACES | REDUCTION THEOREMS | iterated Hardy inequalities | STIELTJES TRANSFORMATION | EMBEDDINGS | INTEGRAL-OPERATORS
Journal Article
Bulletin des sciences mathématiques, ISSN 0007-4497, 05/2016, Volume 140, Issue 4, pp. 86 - 97
In this paper we study some estimates of norms in variable exponent Lebesgue spaces for maximal multiplier operators. We will consider the case when multiplier... 
Spherical maximal function | Variable Lebesgue spaces | Boundedness result | MATHEMATICS, APPLIED | AVERAGES
Journal Article
01/2020
Let $\vec{X}=(X_0, X_1)$ be a compatible couple of Banach spaces, $ 1\le p \le \infty$ and let $ \varphi$ be positive quasi-concave function. Denote by... 
Journal Article
Tokyo Journal of Mathematics, ISSN 0387-3870, 06/2018, Volume 41, Issue 1, pp. 193 - 218
In this paper it is shown that the Hardy-Littlewood maximal operator M is not bounded on Zygmund-Money space M-L(log L),M-lambda,M- O < lambda < n, but M is... 
Morrey spaces | Commutator | BMO | Maximal operator | maximal operator | commutator | MATHEMATICS | WEIGHTED NORM INEQUALITIES | Mathematics - Functional Analysis
Journal Article
Mathematical Inequalities and Applications, ISSN 1331-4343, 10/2017, Volume 20, Issue 4, pp. 901 - 927
In this paper, the boundedness of the composition of the supremal operators defined, for a non-negative measurable functions f on (0,infinity), by S(u)g(t) :=... 
Quasilinear operators | Weights | Iterated Hardy inequalities | FRACTIONAL MAXIMAL OPERATOR | BOUNDEDNESS | weights | MORREY-TYPE SPACES | MONOTONE-FUNCTIONS | INTERPOLATION | MATHEMATICS | WEIGHTED INEQUALITIES | SUBLINEAR-OPERATORS | iterated Hardy inequalities | INTEGRAL-OPERATORS | CONE | Mathematics - Functional Analysis
Journal Article
Journal of Approximation Theory, ISSN 0021-9045, 07/2016, Volume 207, pp. 76 - 97
Let sn(T) denote the nth approximation, isomorphism, Gelfand, Kolmogorov or Bernstein number of the Hardy-type integral operator T given by... 
Banach function spaces | Compact linear operators | Hardy type operators | [formula omitted]-numbers | S-numbers | MATHEMATICS | s-numbers | APPROXIMATION NUMBERS | WIDTHS
Journal Article
Journal of functional analysis, ISSN 0022-1236, 2017, Volume 273, Issue 9, pp. 2939 - 2980
We solve the problem of characterizing weights on (0,∞) for which the inequality involving two possibly different general inner weighted... 
Iterated operators | Weighted inequalities | Embeddings | Classical Lorentz spaces | REARRANGEMENT-INVARIANT NORMS | INEQUALITIES | WEAK-TYPE | MONOTONE-FUNCTIONS | MATHEMATICS | REDUCTION THEOREMS | DUALITY | OPTIMAL SOBOLEV IMBEDDINGS | ASSOCIATE SPACES | CONE | OPERATORS | Computer science | Analysis | Numerical analysis
Journal Article
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, ISSN 0308-2105, 2019, Volume 150, Issue 1, pp. 17 - 39
... on the cone of λ-quasiconcave functions Amiran Gogatishvili Institute of Mathematics of the Czech Academy of Sciences, Žitna 25, 11567 Praha 1, Czech Republic (gogatish... 
Hardy operator | monotone functions | Quasilinear operator | Lebesgue space | weight | quasiconcave functions | integral inequality | Operators (mathematics) | Inequalities
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 04/2013, Volume 286, Issue 5‐6, pp. 579 - 599
Journal Article
Studia Mathematica, ISSN 0039-3223, 2014, Volume 224, Issue 1, pp. 1 - 23
Journal Article
Journal Article
Czechoslovak Mathematical Journal, ISSN 0011-4642, 9/2014, Volume 64, Issue 3, pp. 581 - 597
Journal Article
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