Marcinkiewicz spaces

Ben Zion A. Rubshtein; Genady Ya Grabarnik; Mustafa A. Muratov; Yulia S. Pashkova

doi:10.1007/978-3-319-42758-4_11

Marcinkiewicz spaces

Ben Zion A. Rubshtein, Genady Ya Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

2 Scopus citations

Abstract

In this chapter we study Marcinkiewicz spaces M_V constructed by a quasiconcave weight V. The space M_V is equipped with the norm ∥f∥_MV = ∥V_*f**∥L_∞, where (Formula Presented) dm is the maximal Hardy-Littlewood function of f. We show that (M_V, ∥·∥_MV) is a maximal symmetric space. The associate space (Formula Presented) of every Lorentz space Λ_W with a concave weight W is a Marcinkiewicz space and (Formula Presented). Conversely, the associate space M¹_V coincides with a Lorentz space Λ_W with a concave weight W that is equivalent to V.

Original language	English
Title of host publication	Developments in Mathematics
Publisher	Springer New York LLC
Pages	139-150
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-319-42758-4_11
State	Published - 1 Jan 2016

Publication series

Name	Developments in Mathematics
Volume	45
ISSN (Print)	1389-2177

ASJC Scopus subject areas

General Mathematics

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10.1007/978-3-319-42758-4_11

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abstract = "In this chapter we study Marcinkiewicz spaces MV constructed by a quasiconcave weight V. The space MV is equipped with the norm ∥f∥MV = ∥V*f**∥L∞, where (Formula Presented) dm is the maximal Hardy-Littlewood function of f. We show that (MV, ∥·∥MV) is a maximal symmetric space. The associate space (Formula Presented) of every Lorentz space ΛW with a concave weight W is a Marcinkiewicz space and (Formula Presented). Conversely, the associate space M1V coincides with a Lorentz space ΛW with a concave weight W that is equivalent to V.",

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AU - Rubshtein, Ben Zion A.

AU - Grabarnik, Genady Ya

AU - Muratov, Mustafa A.

AU - Pashkova, Yulia S.

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N2 - In this chapter we study Marcinkiewicz spaces MV constructed by a quasiconcave weight V. The space MV is equipped with the norm ∥f∥MV = ∥V*f**∥L∞, where (Formula Presented) dm is the maximal Hardy-Littlewood function of f. We show that (MV, ∥·∥MV) is a maximal symmetric space. The associate space (Formula Presented) of every Lorentz space ΛW with a concave weight W is a Marcinkiewicz space and (Formula Presented). Conversely, the associate space M1V coincides with a Lorentz space ΛW with a concave weight W that is equivalent to V.

AB - In this chapter we study Marcinkiewicz spaces MV constructed by a quasiconcave weight V. The space MV is equipped with the norm ∥f∥MV = ∥V*f**∥L∞, where (Formula Presented) dm is the maximal Hardy-Littlewood function of f. We show that (MV, ∥·∥MV) is a maximal symmetric space. The associate space (Formula Presented) of every Lorentz space ΛW with a concave weight W is a Marcinkiewicz space and (Formula Presented). Conversely, the associate space M1V coincides with a Lorentz space ΛW with a concave weight W that is equivalent to V.

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DO - 10.1007/978-3-319-42758-4_11

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T3 - Developments in Mathematics

SP - 139

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BT - Developments in Mathematics

PB - Springer New York LLC

ER -

Marcinkiewicz spaces

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