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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

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

  • Czech description

Classification

  • Type

    Jimp - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

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

Basic information

Result type

Jimp - Article in a specialist periodical, which is included in the Web of Science database

Jimp

OECD FORD

Pure mathematics

Year of implementation

2023