Basic functional properties of certain scale of rearrangement-invariant spaces
Result description
We define a new scale of function spaces governed by a norm-like functional based on a combination of a rearrangement-invariant norm, the elementary maximal function, and powers. A particular instance of such spaces surfaced recently in connection with optimality of target function spaces in general Sobolev embeddings involving upper Ahlfors regular measures; however, a thorough analysis of these structures has not been carried out. We present a variety of results on these spaces including their basic functional properties, their relations to customary function spaces and mutual embeddings, and, in a particular situation, a characterization of their associate structures. We discover a new one-parameter path of function spaces leading from a Lebesgue space to a Zygmund class and we compare it to the classical one.
Keywords
rearrangement-invariant spacesmaximal nonincreasing rearrangementLorentz-Zygmund spacesembeddings
The result's identifiers
Result code in IS VaVaI
Result on the web
https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=k6Zko3.Y-h
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Basic functional properties of certain scale of rearrangement-invariant spaces
Original language description
We define a new scale of function spaces governed by a norm-like functional based on a combination of a rearrangement-invariant norm, the elementary maximal function, and powers. A particular instance of such spaces surfaced recently in connection with optimality of target function spaces in general Sobolev embeddings involving upper Ahlfors regular measures; however, a thorough analysis of these structures has not been carried out. We present a variety of results on these spaces including their basic functional properties, their relations to customary function spaces and mutual embeddings, and, in a particular situation, a characterization of their associate structures. We discover a new one-parameter path of function spaces leading from a Lebesgue space to a Zygmund class and we compare it to the classical one.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematische Nachrichten
ISSN
0025-584X
e-ISSN
1522-2616
Volume of the periodical
2023
Issue of the periodical within the volume
296
Country of publishing house
DE - GERMANY
Number of pages
24
Pages from-to
3652-3675.
UT code for WoS article
000975246000001
EID of the result in the Scopus database
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Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Pure mathematics
Year of implementation
2023