A note on Riesz fractional integrals in the limiting case \(\alpha(x)p(x) \equiv n\)

DOI10.2478/s13540-013-0023-xzbMath1312.47045OpenAlexW2080835839MaRDI QIDQ2347312

Stefan G. Samko

Publication date: 27 May 2015

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s13540-013-0023-x

zbMATH Keywords

BMOfractional integralRiesz potentialvariable exponent Lebesgue spacevariable order

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Fractional derivatives and integrals (26A33) Harmonic analysis on homogeneous spaces (43A85) Linear operators on function spaces (general) (47B38)

Related Items (14)

Fractional integrals and derivatives: mapping properties ⋮ Multilinear integral operators in weighted grand Lebesgue spaces ⋮ On weighted generalized fractional and Hardy-type operators acting between Morrey-type spaces ⋮ A note on vanishing Morrey \(\rightarrow\) VMO result for fractional integrals of variable order ⋮ Campanato-Morrey spaces for the double phase functionals with variable exponents ⋮ Dual spaces of anisotropic variable Hardy-Lorentz spaces and their applications ⋮ Grand Lebesgue space for p = ∞ and its application to Sobolev–Adams embedding theorems in borderline cases ⋮ Professor Stefan G. Samko research: a decade retrospective ⋮ Variable exponent fractional integrals in the limiting case \(\alpha (x)p(n) \equiv n\) on quasimetric measure spaces ⋮ Ten equivalent definitions of the fractional Laplace operator ⋮ Extension of Mikhlin multiplier theorem to fractional derivatives and stable processes ⋮ BMO-VMO results for fractional integrals in variable exponent Morrey spaces ⋮ Fractional operators from vanishing Morrey to vanishing Campanato spaces in the variable exponent setting on quasi-metric measure spaces ⋮ Anisotropic variable Campanato-type spaces and their Carleson measure characterizations

Cites Work

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• Lebesgue and Sobolev spaces with variable exponents
• On local summability of Riesz potentials in the case Re \(\alpha >0\)
• Boundedness of translation invariant operators on Hölder spaces and \(L^ p\)-spaces
• The maximal operator on weighted variable Lebesgue spaces
• Weighted estimates of truncated potential kernels in the variable exponent setting
• Convolution and potential type operators inL^p(x)(Rⁿ)
• Convolution type operators inl^p(x)
• On a progress in the theory of lebesgue spaces with variable exponent: maximal and singular operators
• Weighted Norm Inequalities for Fractional Integrals
• Maximal function on generalized Lebesgue spaces L^p(⋅)

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