Boundedness of the maximal, potential and singular operators in the generalized Morrey spaces
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Publication:962439
DOI10.1155/2009/503948zbMath1193.42082OpenAlexW2110853459WikidataQ59219718 ScholiaQ59219718MaRDI QIDQ962439
Publication date: 7 April 2010
Published in: Journal of Inequalities and Applications (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/229089
maximal operatorMorrey spaceRiesz potentialreverse Hölder classCalderón-Zygmund operatorSchrödinger type operator
Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Maximal functions, Littlewood-Paley theory (42B25) Linear operators on function spaces (general) (47B38)
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Cites Work
- Operators of harmonic analysis in weighted spaces with non-standard growth
- A note on Riesz potentials
- \(L^p\) estimates of Schrödinger operators on nilpotent groups
- Fractional integrals on spaces of homogeneous type
- Interior estimates in Morrey spaces for strong solutions to nondivergence form equations with discontinuous coefficients
- Necessary and sufficient conditions for the boundedness of fractional maximal operators in local Morrey-type spaces
- Singular integrals and commutators in generalized Morrey spaces
- On convolution operators leaving \(L^{p,\lambda}\) spaces invariant
- Weighted Sobolev theorem in Lebesgue spaces with variable exponent
- The uncertainty principle
- The Campanato, Morrey and Hölder spaces on spaces of homogeneous type
- Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces
- Hardy-Littlewood Maximal Operator, Singular Integral Operators and the Riesz Potentials on Generalized Morrey Spaces
- A Remark on Estimates for Uniformly Elliptic Operators on WeightedLp Spaces and Morrey Spaces
- Boundedness of integral operators on generalized Morrey spaces and its application to Schrödinger operators
- On the Solutions of Quasi-Linear Elliptic Partial Differential Equations
- Necessary and sufficient conditions for the boundedness of the Riesz potential in local Morrey-type spaces