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Preservation of certain vanishing properties of generalized Morrey spaces by some classical operators
Author(s) -
Alabalik Aysegul Ç,
Almeida Alexandre,
Samko Stefan
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6235
Subject(s) - mathematics , linear subspace , operator theory , singular integral operators , operator norm , pure mathematics , norm (philosophy) , microlocal analysis , fourier integral operator , mathematical analysis , baskakov operator , political science , law
We show that certain vanishing properties defining closed subspaces of generalized Morrey spaces are preserved under the action of various classical operators of harmonic analysis, such as maximal operators, singular‐type operators, Hardy operators, and fractional integral operators. Those vanishing subspaces were recently used to deal with the delicate problem on the description of the closure of nice functions in Morrey norm.