Boundedness of the Riesz potential in local Morrey-type spaces

DOI10.1007/s11118-010-9205-xzbMath1223.42008OpenAlexW2106855696MaRDI QIDQ634197

Victor I. Burenkov, Rza Ch. Mustafayev, Vagif S. Guliyev, Amiran Gogatishvili

Publication date: 2 August 2011

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11118-010-9205-x

zbMATH Keywords

Riesz potential Hardy operator on the cone of monotonic functions local and global Morrey-type spaces

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Function spaces arising in harmonic analysis (42B35)

Related Items (53)

Nonhomogeneous central Morrey-type spaces in \(L^{p(\cdot)}\) and weak estimates for the maximal and Riesz potential operators ⋮ Boundedness of fractional integral operators containing Mittag-Leffler functions via \((s,m)\)-convexity ⋮ Growth properties near the origin for generalized Riesz potentials ⋮ Anisotropic fractional maximal commutators with BMO functions on anisotropic Morrey-type spaces ⋮ Necessary and sufficient condition for the boundedness of the Gegenbauer-Riesz potential on Morrey spaces ⋮ Parabolic sublinear operators with rough kernel generated by parabolic Calderón-Zygmund operators and parabolic local Campanato space estimates for their commutators on the parabolic generalized local Morrey spaces ⋮ BOUNDEDNESS OF THE GENERALIZED RIESZ POTENTIAL IN LOCAL MORREY TYPE SPACES ⋮ An analog of Young's inequality for convolutions of functions for general Morrey-type spaces ⋮ Boundedness of maximal operators and Sobolev's inequality on non-homogeneous central Musielak-Orlicz-Morrey spaces ⋮ Growth properties for Riesz potentials of functions in weighted variable \(L^{p(\cdot)}\) spaces ⋮ Generalized fractional maximal operator on generalized local Morrey spaces ⋮ Generalized local Morrey spaces and fractional integral operators with rough kernel ⋮ Boundedness for the modified fractional integral operator from mixed Morrey spaces to the bounded mean oscillation space and Lipschitz spaces ⋮ Decompositions of local Morrey-type spaces ⋮ Boundedness of the maximal operator and Sobolev's inequality on non-homogeneous central Herz-Morrey-Orlicz spaces ⋮ Weighted estimates for a class of sublinear operators ⋮ Hardy–Sobolev inequality for Sobolev functions in central Herz–Morrey spaces ⋮ On boundedness of the generalized Riesz potential in local Morrey-type spaces ⋮ Boundedness of sublinear operators and commutators on generalized Morrey spaces ⋮ Generalized fractional integral operators on variable exponent Morrey type spaces over metric measure spaces ⋮ Hardy and Sobolev inequalities in the half space ⋮ Weak estimates for the maximal and Riesz potential operators on non-homogeneous central Morrey type spaces in L^1 over metric measure spaces ⋮ Applications of Littlewood-Paley theory for \(\dot{B}_\sigma\)-Morrey spaces to the boundedness of integral operators ⋮ Sobolev embeddings for generalized Riesz potentials of functions in Morrey spaces \(L^{(1, \varphi)}(G)\) over nondoubling measure spaces ⋮ Growth properties of potentials in central Morrey–Orlicz spaces on the unit ball ⋮ Stein-Weiss inequalities for radial local Morrey spaces ⋮ Boundedness of some sublinear operators and their commutators on generalized local Morrey spaces ⋮ On weighted Hardy inequalities in mixed norms ⋮ Local sharp maximal functions, geometrical maximal functions and rough maximal functions on local Morrey spaces with variable exponents ⋮ The weighted inequalities for a certain class of quasilinear integral operators on the cone of monotone functions ⋮ Sobolev's inequalities for Herz-Morrey-Orlicz spaces on the half space ⋮ Boundedness of maximal operator, Hardy operator and Sobolev's inequalities on non-homogeneous central Herz-Morrey-Musielak-Orlicz spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On weighted iterated Hardy-type inequalities ⋮ Boundedness of the anisotropic Riesz potential in anisotropic local Morrey-type spaces ⋮ Spherical limits for Riesz potentials of functions in central generalized Orlicz-Morrey spaces on the unit ball ⋮ Boundedness of quasilinear integral operators on the cone of monotone functions ⋮ On the Boundedness of the Fractional Maximal Operator, Riesz Potential and Their Commutators in Generalized Morrey Spaces ⋮ Equivalence of norms of Riesz potential and fractional maximal function in generalized Morrey spaces ⋮ Sublinear operators with rough kernel generated by Calderón-Zygmund operators and their commutators on generalized local Morrey spaces ⋮ Characterizations of some operators on the vanishing generalized Morrey spaces with variable exponent ⋮ Marcinkiewicz-type interpolation theorem for Morrey-type spaces and its corollaries ⋮ Hardy–Sobolev inequalities for Sobolev functions in central Herz–Morrey spaces on the unit ball ⋮ Boundedness of the maximal and potential operators in Herz-Morrey type spaces ⋮ Unnamed Item ⋮ Weak estimates for the maximal and Riesz potential operators in non-homogeneous central Herz-Morrey spaces ⋮ Herz–Morrey spaces of variable exponent, Riesz potential operator and duality ⋮ HERZ–MORREY SPACES ON THE UNIT BALL WITH VARIABLE EXPONENT APPROACHING AND DOUBLE PHASE FUNCTIONALS ⋮ Stein-Weiss inequality for local mixed radial-angular Morrey spaces ⋮ Boundedness of the Riesz potential in central Morrey-Orlicz spaces ⋮ The boundedness of fractional integral operators in local and global mixed Morrey-type spaces

Cites Work

This page was built for publication: Boundedness of the Riesz potential in local Morrey-type spaces