On a characterisation of the space of Riesz potential of functions in Banach spaces with some a priori properties

DOI10.23671/VNC.2018.2.14726zbMath1464.46036OpenAlexW3191392586MaRDI QIDQ4970051

Stefan G. Samko, Salaudin Umarkhadzhiev

Publication date: 14 October 2020

Published in: Владикавказский математический журнал (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/vmj658

zbMATH Keywords

distributionsOrlicz spacehypersingular integralRiesz potentialgrand Lebesgue spaceidentity approximationspace of Riesz potentialsLizorkin test functions spacevariable order Lebesgue space

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) Integral transforms in distribution spaces (46F12)

Cites Work

• Variable Lebesgue spaces. Foundations and harmonic analysis
• Generalization of the notion of grand Lebesgue space
• Integral operators in non-standard function spaces. Volume 1: Variable exponent Lebesgue and amalgam spaces
• Lebesgue and Sobolev spaces with variable exponents
• Characterization of Riesz and Bessel potentials on variable Lebesgue spaces
• Description of the space of Riesz potentials of functions in a grand Lebesgue space on \(\mathbb{R}^n\)
• Fractional integrals and derivatives: mapping properties
• Riesz fractional integrals in grand Lebesgue spaces on \(\mathbb{R}^{n}\)
• On grand Lebesgue spaces on sets of infinite measure
• Integral inequalities with weights for the Hardy maximal function
• The characterization of functions arising as potentials
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