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Integral Equations and Operator Theory, ISSN 0378-620X, 2/2018, Volume 90, Issue 1, pp. 1 - 33
We define Euler–Hilbert–Sobolev spaces and obtain embedding results on homogeneous groups using Euler operators, which are homogeneous differential operators... 
Euler–Hilbert–Sobolev space | Homogeneous Lie group | Analysis | Rellich inequality | Hardy inequality | Weighted Sobolev inequality | Mathematics | Secondary 46E35 | Sobolev inequality | Primary 22E30 | Sobolev–Lorentz–Zygmund space | MATHEMATICS | REMAINDER | RELLICH INEQUALITIES | Euler-Hilbert-Sobolev space | HARDY | Sobolev-Lorentz-Zygmund space | Anisotropy
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 10/2019, Volume 277, Issue 7, pp. 2381 - 2441
In this work we present a newly developed study of the interpolation of weighted Sobolev spaces by the complex method. We show that in some cases, one can... 
Complex interpolation spaces | Weighted Sobolev spaces | Stein Weiss theorem | MATHEMATICS | ENTROPY NUMBERS | EIGENVALUE DISTRIBUTIONS
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 11/2018, Volume 370, Issue 11, pp. 8285 - 8310
We prove scaling invariant Gagliardo-Nirenberg type inequalities of the form \displaystyle \Vert\varphi \Vert _{L^p(\mathbb{R}^d)}\le... 
Interpolation inequalities | Radial symmetry | Coulomb energy | Fractional Sobolev inequality | Riesz potential | RADIAL FUNCTIONS | ENERGY | STABILITY | MOLECULES | INTEGRALS | MATHEMATICS | WEIGHTED INEQUALITIES | SYMMETRY | THOMAS-FERMI | fractional Sobolev inequality | radial symmetry | SYSTEMS | ATOMS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2016, Volume 433, Issue 1, pp. 149 - 175
In this work we consider the initial value problem (IVP) associated to the two dimensional Zakharov–Kuznetsov... 
Local well-posedness | Zakharov–Kuznetsov equation | Weighted Sobolev spaces | Zakharov-Kuznetsov equation | MATHEMATICS | MATHEMATICS, APPLIED | BENJAMIN-ONO-EQUATION | IVP | CAUCHY-PROBLEM | WELL-POSEDNESS
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 04/2020, Volume 193, p. 111505
We characterize one-sided weighted Sobolev spaces $W^{1,p}(\mathbb{R},\omega)$, where $\omega$ is a one-sided Sawyer weight, in terms of a.e.~and weighted... 
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 17
Optimal asymptotic orders of the probabilistic linear ( n , δ ) $(n,\delta)$ -widths of λ n , δ ( W 2 , α , β r , ν , L q , α , β ) $\lambda_{n,\delta... 
28C20 | 41A46 | 41A25 | Gaussian measure | probabilistic linear widths | Analysis | Mathematics, general | Mathematics | weighted Sobolev classes | Applications of Mathematics | Jacobi weights | 42C15 | MATHEMATICS | MATHEMATICS, APPLIED | Sobolev space
Journal Article
Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, 2018, Volume 43, pp. 885 - 903
We obtain improved fractional Poincare and Sobolev-Poincare inequalities including powers of the distance to the boundary in bounded John, s-John, and... 
Cusp domains | John domains | S-John domains | Sobolev inequality | Fractional norms | Weighted Sobolev spaces | Poincaré inequality | fractional norms | WEIGHTED POINCARE | MATHEMATICS | s-John domains | Poincare inequality | weighted Sobolev spaces | cusp domains
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 02/2020, Volume 191, p. 111635
We consider a nonlinear pseudo-differential equation driven by the fractional p-Laplacian (−Δ)ps with s∈(0,1) and p⩾2 (degenerate case), under Dirichlet type... 
Fractional [formula omitted]-Laplacian | Weighted Hölder regularity | Boundary regularity | Fractional Sobolev spaces | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | OPERATOR | REGULARITY | CONCAVE | Fractional p-Laplacian | DIRICHLET PROBLEM | Weighted Holder regularity | Sobolev space | Dirichlet problem | Differential equations
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2018, Volume 460, Issue 2, pp. 1004 - 1018
In this work we consider the initial value problem (IVP) associated to the Ostrovsky equationsut+∂x3u±∂x−1u+u∂xu=0,x∈R,t∈R,u(x,0)=u0(x).} We study the... 
Ostrovsky equation | Local well-posedness | Weighted Sobolev spaces | MATHEMATICS | MATHEMATICS, APPLIED | BENJAMIN-ONO-EQUATION | REGULARITY | CAUCHY-PROBLEM | WELL-POSEDNESS | KDV EQUATION
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 5/2015, Volume 82, Issue 1, pp. 1 - 32
In this paper, we characterize operator-theoretic properties (boundedness, compactness, and Schatten class membership) of Toeplitz operators with positive... 
weighted Fock space | Analysis | Mathematics | Toeplitz operator | Fock–Sobolev space | Primary 47B35 | Secondary 32A25 | 30H20 | Schatten class | MATHEMATICS | Fock-Sobolev space
Journal Article
Numerische Mathematik, ISSN 0029-599X, 2/2019, Volume 141, Issue 2, pp. 399 - 427
Journal Article
Nonlinear Analysis, Theory, Methods and Applications, ISSN 0362-546X, 06/2015, Volume 119, pp. 354 - 381
Abstract We give short simple proofs of UspenskiѤs results characterizing Besov spaces as trace spaces of weighted Sobolev spaces. We generalize UspenskiѤs... 
Littlewood-Paley decompositions | Trace theory | Besov spaces | Functional calculus | Weighted Sobolev spaces | DISTRIBUTIONS | MATHEMATICS | MATHEMATICS, APPLIED | BESOV | TEMPERATURES | LIPSCHITZ SPACES | EUCLIDEAN N-SPACE | Nonlinearity | Calculus | Sobolev space | Mathematical analysis | Optimization | Proving | Functional Analysis | Mathematics
Journal Article
Complex Analysis and Operator Theory, ISSN 1661-8254, 8/2014, Volume 8, Issue 6, pp. 1225 - 1256
Journal Article
Computational Methods and Function Theory, ISSN 1617-9447, 9/2019, Volume 19, Issue 3, pp. 473 - 486
In this paper, we provide a concrete criterion for sets lying in a hyperplane to be removable for weighted Orlicz–Sobolev spaces. We define porous sets and... 
Removable sets | Weighted orlicz–sobolev spaces | Computational Mathematics and Numerical Analysis | Functions of a Complex Variable | Analysis | Mathematics | Porosity | 31B15 | MATHEMATICS | Weighted orlicz-sobolev spaces | MATHEMATICS, APPLIED | THEOREMS
Journal Article
Complex Analysis and Operator Theory, ISSN 1661-8254, 8/2017, Volume 11, Issue 6, pp. 1451 - 1461
We determine the spectrum of the Voltterra-type integral operators $$V_g$$ V g on the growth type Fock–Sobolev spaces $$\mathcal {F}_{\psi _m}^\infty $$ F ψ m... 
47B33 | Mathematics | Fock–Sobolev spaces | 30H20 | Spectrum | Volterra-type integral operators | Operator Theory | Bounded | Secondary 46E22 | Analysis | 46E20 | Primary 47B32 | Mathematics, general | Weighted Fock spaces | Compact | MATHEMATICS | MATHEMATICS, APPLIED | Fock-Sobolev spaces
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 11/2015, Volume 128, pp. 248 - 272
A complete description of traces on Rn of functions from the weighted Sobolev space W1l(Rn+1,γ), l∈N, with weight γ∈A1loc(Rn+1) is obtained. In the case l=1... 
Besov spaces of variables smoothness | Traces | Muckenhoupt weights | Weighted Sobolev spaces | MATHEMATICS | MATHEMATICS, APPLIED | Algorithms
Journal Article
Journal of Complexity, ISSN 0885-064X, 08/2019, Volume 53, pp. 95 - 112
We study multivariate approximation for complex-valued functions defined over the d-dimensional torus, these functions belonging to weighted standard Sobolev... 
Tractability | Weighted Sobolev space | Information-based complexity | Multivariate approximation
Journal Article
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2016, Volume 443, Issue 1, pp. 566 - 584
We consider the well-posedness of the initial value problem associated to the k-generalized Zakharov–Kuznetsov equation in fractional weighted Sobolev spaces... 
Generalized Zakharov–Kuznetsov | Weighted Sobolev spaces | MATHEMATICS | MATHEMATICS, APPLIED | BENJAMIN-ONO-EQUATION | IVP | CAUCHY-PROBLEM | Generalized Zakharov-Kuznetsov | Anisotropy
Journal Article
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