On a littlewood-paley theorem and connections between some non-isotropic distributions spaces.

B. Bordin; D. L. Fernández

Displaying similar documents to “On a littlewood-paley theorem and connections between some non-isotropic distributions spaces.”

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Refined Hardy inequalities

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The aim of this article is to present “refined” Hardy-type inequalities. Those inequalities are generalisations of the usual Hardy inequalities, their additional feature being that they are invariant under oscillations: when applied to highly oscillatory functions, both sides of the refined inequality are of the same order of magnitude. The proof relies on paradifferential calculus and Besov spaces. It is also adapted to the case of the Heisenberg group.

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Complex Interpolation and Fourier Multipliers for the Spaces B.... and F.... of Besov-Hardy-Sobolev Type: The Case 0<p....., 0<q.... .

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Soulaymane Korry (2002)

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We describe a class O of nonlinear operators which are bounded on the Lizorkin-Triebel spaces F (R), for 0 < s < 1 and 1 < p, q < ∞. As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on F (R), for 0 < s < 1 and 1 < p, q < ∞ ; this extends the result of Kinnunen (1997), valid for the Sobolev space H (R).

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Sun Qiyu (1994)

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Extension by integer translates of compactly supported function for multiplier spaces on periodic Hardy spaces to multiplier spaces on Hardy spaces is given. Shannon sampling theorem is extended to Hardy spaces.

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On the Choquet integrals associated to Bessel capacities

Keng Hao Ooi (2022)

Czechoslovak Mathematical Journal

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We characterize the Choquet integrals associated to Bessel capacities in terms of the preduals of the Sobolev multiplier spaces. We make use of the boundedness of local Hardy-Littlewood maximal function on the preduals of the Sobolev multiplier spaces and the minimax theorem as the main tools for the characterizations.

A Marcinkiewicz type multiplier theorem for H¹ spaces on product domains

Michał Wojciechowski (2000)

Studia Mathematica

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It is proved that if $m : ℝ^{d} \to ℂ$ satisfies a suitable integral condition of Marcinkiewicz type then m is a Fourier multiplier on the $H^{1}$ space on the product domain $ℝ^{d_{1}} \times . . . \times ℝ^{d_{k}}$ . This implies an estimate of the norm $N (m, L^{p} (ℝ^{d})$ of the multiplier transformation of m on $L^{p} (ℝ^{d})$ as p→1. Precisely we get $N (m, L^{p} (ℝ^{d})) ≲ {(p - 1)}^{- k}$ . This bound is the best possible in general.

A note on the Marcinkiewicz integral

Alberto Torchinsky, Shilin Wang (1990)

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