On boundedness of maximal functions in Sobolev spaces.

Hajłasz, Piotr; Onninen, Jani

Displaying similar documents to “On boundedness of maximal functions in Sobolev spaces.”

Characterization of rearrangement invariant spaces with fixed points for the Hardy-Littlewood maximal operator.

Martín, Joaquim, Soria, Javier (2006)

Annales Academiae Scientiarum Fennicae. Mathematica

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Lebesgue points in variable exponent spaces.

Harjulehto, Petteri, Hästö, Peter (2004)

Annales Academiae Scientiarum Fennicae. Mathematica

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Spherical harmonics and maximal estimates for the Schrödinger equation.

Sjölin, Per (2005)

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Hölder quasicontinuity in variable exponent Sobolev spaces.

Harjulehto, Petteri, Kinnunen, Juha, Tuhkanen, Katja (2007)

Journal of Inequalities and Applications [electronic only]

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Decay for travelling waves in the Gross–Pitaevskii equation

Philippe Gravejat (2004)

Annales de l'I.H.P. Analyse non linéaire

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On the boundedness of the maximal operator and singular integral operators in generalized Morrey spaces

Ali Akbulut, Vagif Guliyev, Rza Mustafayev (2012)

Mathematica Bohemica

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In the paper we find conditions on the pair $(ω_{1}, ω_{2})$ which ensure the boundedness of the maximal operator and the Calderón-Zygmund singular integral operators from one generalized Morrey space $ℳ_{p, ω_{1}}$ to another $ℳ_{p, ω_{2}}$ , $1 < p < \infty$ , and from the space $ℳ_{1, ω_{1}}$ to the weak space $W ℳ_{1, ω_{2}}$ . As applications, we get some estimates for uniformly elliptic operators on generalized Morrey spaces.

Commutators of the fractional maximal function on variable exponent Lebesgue spaces

Pu Zhang, Jianglong Wu (2014)

Czechoslovak Mathematical Journal

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Let $M_{β}$ be the fractional maximal function. The commutator generated by $M_{β}$ and a suitable function $b$ is defined by $[M_{β}, b] f = M_{β} (b f) - b M_{β} (f)$ . Denote by $𝒫 (ℝ^{n})$ the set of all measurable functions $p (\cdot) : ℝ^{n} \to [1, \infty)$ such that $1 < p_{-} : = \underset{x \in ℝ^{n}}{ess \inf} p (x) and p_{+} : = \underset{x \in ℝ^{n}}{ess \sup} p (x) < \infty,$ and by $ℬ (ℝ^{n})$ the set of all $p (\cdot) \in 𝒫 (ℝ^{n})$ such that the Hardy-Littlewood maximal function $M$ is bounded on $L^{p (\cdot)} (ℝ^{n})$ . In this paper, the authors give some characterizations of $b$ for which $[M_{β}, b]$ is bounded from $L^{p (\cdot)} (ℝ^{n})$ into $L^{q (\cdot)} (ℝ^{n})$ , when $p (\cdot) \in 𝒫 (ℝ^{n})$ , $0 < β < n / p_{+}$ and $1 / q (\cdot) = 1 / p (\cdot) - β / n$ with $q (\cdot) (n - β) / n \in ℬ (ℝ^{n})$ .

Existence of positive solutions for some polyharmonic nonlinear equations in $ℝ^{n}$ .

Mâagli, Habib, Zribi, Malek (2006)

Abstract and Applied Analysis

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