The maximal operator in Lebesgue spaces with variable exponent near 1

DOI10.1002/mana.200410465zbMath1125.46021OpenAlexW2138794150MaRDI QIDQ3427402

Peter A. Hästö

Publication date: 20 March 2007

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.200410465

zbMATH Keywords

Lebesgue spacemaximal operatorvariable exponent

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) Maximal functions, Littlewood-Paley theory (42B25)

Related Items (10)

Modular inequalities for the maximal operator in variable Lebesgue spaces ⋮ Construction of function spaces close to \(L^\infty \) with associate space close to \(L^1\) ⋮ Boundedness of maximal operators on Herz spaces with radial variable exponent ⋮ Sobolev's inequalities and vanishing integrability for Riesz potentials of functions in the generalized Lebesgue space \(L^{p(\cdot)}(\log L)^{q(\cdot)}\) ⋮ Maximal operator on variable Lebesgue spaces for almost monotone radial exponent ⋮ Minimizers of the variable exponent, non-uniformly convex Dirichlet energy ⋮ Integrability of maximal functions and Riesz potentials in Orlicz spaces of variable exponent ⋮ 𝐿log𝐿 results for the maximal operator in variable 𝐿^{𝑝} spaces ⋮ HERZ–MORREY SPACES ON THE UNIT BALL WITH VARIABLE EXPONENT APPROACHING AND DOUBLE PHASE FUNCTIONALS ⋮ Combined concave-convex effects in anisotropic elliptic equations with variable exponent

Cites Work

• Unnamed Item
• Commutators of singular integrals on generalized \(L^p\) spaces with variable exponent
• An example of a space of \(L^{p(x)}\) on which the Hardy-Littlewood maximal operator is not bounded
• Maximal and fractional operators in weighted \(L^{p(x)}\) spaces
• A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces
• A trace inequality for generalized potentials in Lebesgue spaces with variable exponent
• Singular integrals and potentials in some Banach function spaces with variable exponent
• Gradient estimates for thep(x)-Laplacean system

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