Boundedness of maximal operators and potential operators on Carleson curves in Lebesgue spaces with variable exponent

DOI10.1007/s10114-008-6464-1zbMath1151.42006OpenAlexW2014350792MaRDI QIDQ960598

Vakhtang Kokilashvili, Stefan G. Samko

Publication date: 5 January 2009

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-008-6464-1

zbMATH Keywords

fractional integralsvariable exponentsingular operatorSobolev theoremweighted generalized Lebesgue spaces

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Integral operators (45P05) Linear operators on function spaces (general) (47B38)

Related Items (18)

The Plemelj–Privalov theorem in variable exponent Clifford analysis ⋮ Fractional and hypersingular operators in variable exponent spaces on metric measure spaces ⋮ On the regularization of a multidimensional integral equation in Lebesgue spaces with variable exponent ⋮ Fractional integration and differentiation of variable order: an overview ⋮ Variable exponent Herz spaces ⋮ Characterizations for the fractional maximal operators on Carleson curves in local generalized Morrey spaces ⋮ On the boundedness of Marcinkiewicz integrals on continual variable exponent Herz spaces ⋮ Potential operators in modified Morrey spaces defined on Carleson curves ⋮ Some new Stein and Hardy type inequalities ⋮ Two-weight inequalities for the maximal operator in a Lebesgue space with variable exponent ⋮ Some properties of the potential operators in Morrey spaces defined on Carleson curves ⋮ The regularity of local solutions for a generalized Camassa-Holm type equation ⋮ Characterization of the variable exponent Bessel potential spaces via the Poisson semigroup ⋮ On singular integral operators with semi-almost periodic coefficients on variable Lebesgue spaces ⋮ Generalized potentials in variable exponent Lebesgue spaces on homogeneous spaces ⋮ Operators of harmonic analysis in weighted spaces with non-standard growth ⋮ Characterizations for the potential operators on Carleson curves in local generalized Morrey spaces ⋮ The Cauchy Singular Integral Operator on Weighted Variable Lebesgue Spaces

Cites Work

• Amemiya norm equals Orlicz norm in Musielak--Orlicz spaces
• On some variational problems
• Carleson curves, Muckenhoupt weights, and Toeplitz operators
• On Sobolev theorem for Riesz-type potentials in Lebesgue spaces with variable exponent
• Maximal and fractional operators in weighted \(L^{p(x)}\) spaces
• Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spacesLp(·) andWk,p(·)
• Convolution and potential type operators inL^p(x)(Rⁿ)
• Maximal function on generalized Lebesgue spaces L^p(⋅)
• The regularity of Lagrangiansf(x, ξ)=254-01254-01254-01with Hölder exponents α(x)
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Boundedness of maximal operators and potential operators on Carleson curves in Lebesgue spaces with variable exponent