Displaying similar documents to “ H p spaces over open subsets of R n ”

Distribution and rearrangement estimates of the maximal function and interpolation

Irina Asekritova, Natan Krugljak, Lech Maligranda, Lars-Erik Persson (1997)

Studia Mathematica

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There are given necessary and sufficient conditions on a measure dμ(x)=w(x)dx under which the key estimates for the distribution and rearrangement of the maximal function due to Riesz, Wiener, Herz and Stein are valid. As a consequence, we obtain the equivalence of the Riesz and Wiener inequalities which seems to be new even for the Lebesgue measure. Our main tools are estimates of the distribution of the averaging function f** and a modified version of the Calderón-Zygmund decomposition....

A weighted version of Journé's lemma.

Donald Krug, Alberto Torchinsky (1994)

Revista Matemática Iberoamericana

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In this paper we discuss a weighted version of Journé's covering lemma, a substitution for Whitney decomposition of an open set in R where squares are replaced by rectangles. We then apply this result to obtain a sharp version of the atomic decomposition of the weighted Hardy spaces H (R x R ) and a description of their duals when p is close to 1.

A sharp rearrangement inequality for the fractional maximal operator

A. Cianchi, R. Kerman, B. Opic, L. Pick (2000)

Studia Mathematica

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We prove a sharp pointwise estimate of the nonincreasing rearrangement of the fractional maximal function of ⨍, M γ ⨍ , by an expression involving the nonincreasing rearrangement of ⨍. This estimate is used to obtain necessary and sufficient conditions for the boundedness of M γ between classical Lorentz spaces.

An atomic decomposition of the predual of BMO(ρ).

Beatriz E. Viviani (1987)

Revista Matemática Iberoamericana

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We study the Orlicz type spaces H, defined as a generalization of the Hardy spaces H for p ≤ 1. We obtain an atomic decomposition of H, which is used to provide another proof of the known fact that BMO(ρ) is the dual space of H (see S. Janson, 1980, [J]).

Partial retractions for weighted Hardy spaces

Sergei Kisliakov, Quanhua Xu (2000)

Studia Mathematica

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Let 1 ≤ p ≤ ∞ and let w 0 , w 1 be two weights on the unit circle such that l o g ( w 0 w 1 - 1 ) ∈ B M O . We prove that the couple ( H p ( w 0 ) , H p ( w 1 ) ) of weighted Hardy spaces is a partial retract of ( L p ( w 0 ) , L p ( w 1 ) ) . This completes previous work of the authors. More generally, we have a similar result for finite families of weighted Hardy spaces. We include some applications to interpolation.

CLO spaces and central maximal operators

Martha Guzmán-Partida (2013)

Archivum Mathematicum

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We consider central versions of the space BLO studied by Coifman and Rochberg and later by Bennett, as well as some natural relations with a central version of a maximal operator.