The Cauchy integral operator on the predual of a Morrey space.

Ruan, Jianmiao; Chen, Jiecheng

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Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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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 $q (\cdot) (n - β) / n \in ℬ (ℝ^{n})$ .

Continuity of multilinear operators on Triebel-Lizorkin spaces.

Liu, Lanzhe (2006)

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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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