𝐿log𝐿 results for the maximal operator in variable 𝐿^{𝑝} spaces

DOI10.1090/S0002-9947-08-04608-4zbMath1163.42006MaRDI QIDQ3625578

Alberto Fiorenza, David V. Cruz-Uribe

Publication date: 5 May 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

maximal operatorvariable Lebesgue space

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Function spaces arising in harmonic analysis (42B35)

Related Items (22)

Modular inequalities for the maximal operator in variable Lebesgue spaces ⋮ Construction of function spaces close to \(L^\infty \) with associate space close to \(L^1\) ⋮ Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials ⋮ A modular variable Orlicz inequality for the local maximal operator ⋮ Sobolev embeddings for Riesz potential spaces of variable exponents near 1 and Sobolev's exponent ⋮ A trace inequality of Riesz potentials in variable exponent Orlicz spaces ⋮ Maximal functions, Riesz potentials and Sobolev embeddings on Musielak-Orlicz-Morrey spaces of variable exponent in \(\mathbb{R}^n\) ⋮ Partial regularity for minimizers of a class of non autonomous functionals with nonstandard growth ⋮ Sobolev inequalities for Musielak-Orlicz spaces ⋮ Doob's maximal inequality and Burkholder-Davis-Gundy's inequality on Musielak-Orlicz spaces ⋮ On the boundary limits of monotone Sobolev functions in variable exponent Orlicz spaces ⋮ Martingale inequalities on Musielak–Orlicz Hardy spaces ⋮ Embeddings between grand, small, and variable Lebesgue spaces ⋮ Extrapolation and interpolation in generalized Orlicz spaces ⋮ Weighted norm inequalities for the maximal operator on variable Lebesgue spaces ⋮ Maximal operator on Orlicz spaces of two variable exponents over unbounded quasi-metric measure spaces ⋮ Sobolev's inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space \(L^{p(\cdot)}(\log L)^{q(\cdot)}\) ⋮ Weighted Sobolev inequality in Musielak-Orlicz space ⋮ Fractional maximal operator on Musielak-Orlicz spaces over unbounded quasi-metric measure spaces ⋮ SOBOLEV INEQUALITIES FOR ORLICZ SPACES OF TWO VARIABLE EXPONENTS ⋮ On some questions related to the maximal operator on variable 𝐿^{𝑝} spaces ⋮ Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponents

Cites Work

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• Orlicz spaces and modular spaces
• Weighted weak type inequalities with variable exponents for Hardy and maximal operators
• The fractional maximal operator and fractional integrals on variable \(L^p\) spaces
• Maximal functions for Lebesgue spaces with variable exponent approaching 1
• Maximal functions on Musielak--Orlicz spaces and generalized Lebesgue spaces
• The ergodic theorem
• The maximal operator in Lebesgue spaces with variable exponent near 1
• Approximate identities in variableLp spaces
• Maximal function on generalized Lebesgue spaces L^p(⋅)
• Hardy-Littlewood maximal operator on L^p(x) (ℝ)
• Note on the class LlogL

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