Growth properties of Musielak-Orlicz integral means for Riesz potentials

DOI10.1016/j.na.2014.09.012zbMath1333.46030OpenAlexW2049935118MaRDI QIDQ468612

Yoshihiro Mizuta, Fumi-Yuki Maeda, Tetsu Shimomura

Publication date: 7 November 2014

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2014.09.012

zbMATH Keywords

Musielak-Orlicz spacevariable exponentRiesz potentials

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) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)

Related Items (12)

Growth properties near the origin for generalized Riesz potentials ⋮ Hardy and Sobolev inequalities for double phase functionals on the unit ball ⋮ Growth properties for Riesz potentials of functions in weighted variable \(L^{p(\cdot)}\) spaces ⋮ Campanato-Morrey spaces for the double phase functionals with variable exponents ⋮ Hardy-Sobolev inequalities for double phase functionals ⋮ Vanishing exponential integrability for Riesz potentials in Morrey–Orlicz spaces ⋮ Sobolev's inequality for Musielak-Orlicz-Sobolev functions ⋮ Hardy-Littlewood-Sobolev theorem for variable Riesz potentials ⋮ Growth properties of potentials in central Morrey–Orlicz spaces on the unit ball ⋮ Campanato-Morrey spaces for the double phase functionals ⋮ Spherical limits for Riesz potentials of functions in central generalized Orlicz-Morrey spaces on the unit ball ⋮ Boundedness of fractional maximal operators for double phase functionals with variable exponents

Cites Work

• Maximal functions, Riesz potentials and Sobolev embeddings on Musielak-Orlicz-Morrey spaces of variable exponent in \(\mathbb{R}^n\)
• Capacity for potentials of functions in Musielak-Orlicz spaces
• Orlicz spaces and modular spaces
• Local-to-global results in variable exponent spaces
• Sobolev's inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space \(L^{p(\cdot)}(\log L)^{q(\cdot)}\)
• Semi-fine limits and semi-fine differentiability of Riesz potentials of functions in \(L^ p\).
• \(L^ q\)-mean limits for Taylor's expansion of Riesz potentials of functions in Orlicz classes
• Boundedness of maximal operators and Sobolev's inequality on Musielak-Orlicz-Morrey spaces
• Weighted Sobolev theorem in Lebesgue spaces with variable exponent
• Weakly Differentiable Functions
• Maximal function on generalized Lebesgue spaces L^p(⋅)
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