Continuity properties of Riesz potentials of Orlicz functions

DOI10.2748/tmj/1245849445zbMath1181.46026OpenAlexW2042935585MaRDI QIDQ843031

Tetsu Shimomura, Yoshihiro Mizuta

Publication date: 29 September 2009

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1245849445

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)

Related Items (19)

Sobolev-type inequalities on variable exponent Morrey spaces of an integral form ⋮ Orlicz-Sobolev capacity of balls ⋮ Generalized fractional integral operators on variable exponent Morrey spaces of an integral form ⋮ Maximal functions, Riesz potentials and Sobolev embeddings on Musielak-Orlicz-Morrey spaces of variable exponent in \(\mathbb{R}^n\) ⋮ Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces ⋮ Exponential integrability of Riesz potentials of Orlicz functions ⋮ Musielak-Orlicz-Sobolev spaces on metric measure spaces ⋮ Atomic decompositions of Hardy spaces with variable exponents and its application to bounded linear operators ⋮ Sobolev's inequality in Musielak–Orlicz–Morrey spaces of an integral form ⋮ Trudinger's inequality and continuity of potentials on Musielak-Orlicz-Morrey spaces ⋮ Boundedness of integral operators of double phase ⋮ Trudinger's inequality for Riesz potentials of functions in Musielak-Orlicz spaces ⋮ Trudinger's inequality and continuity for Riesz potentials of functions in Musielak-Orlicz-Morrey spaces on metric measure spaces ⋮ Weighted Sobolev inequality in Musielak-Orlicz space ⋮ Sobolev's inequality for Riesz potentials of functions in Morrey spaces of integral form ⋮ Weighted Orlicz-Riesz capacity of balls ⋮ Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponents ⋮ On Trudinger-type Inequalities in Orlicz-Morrey Spaces of an Integral Form ⋮ Riesz potentials and Sobolev-type inequalities in Orlicz-Morrey spaces of an integral form

Cites Work

• Vanishing exponential integrability for Riesz potentials of functions in Orlicz classes
• Continuity properties of potentials and Beppo-Levi-Deny functions
• Exponential integrability for Riesz potentials of functions in Orlicz classes
• Vanishing exponential integrability for functions whose gradients belong to \(L^n(\log(e+L))^{\alpha}\)
• Differentiability properties of Orlicz-Sobolev functions
• Continuity properties of Riesz potentials and boundary limits of Beppo Levi functions.
• Strong and Weak Type Inequalities for Some Classical Operators in Orlicz Spaces
• Differentiability and Holder continuity of Riesz potentials of Orlicz functions
• Sharpness of embeddings in logarithmic Bessel-potential spaces
• On Certain Convolution Inequalities
• A Theory of Capacities for Potentials of Functions in Lebesgue Classes.
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