Published January 1, 2023
| Version v1
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Grand Lebesgue Spaces with Mixed Local and Global Aggrandization and the Maximal and Singular Operators
Creators
- 1. United Arab Emirates Univ, Coll Sci, Dept Math Sci, PO Box 15551, Al Ain, U Arab Emirates
Description
The approach to "locally" aggrandize Lebesgue spaces, previously suggested by the authors and based on the notion of "aggrandizer", is combined with the usual "global" aggrandization. We study properties of such spaces including embeddings, dependence of the choice of the aggrandizer and, in particular, we discuss the question when these spaces are not new, coinciding with globally aggrandized spaces, and when they proved to be new. We study the boundedness of the maximal, singular, and maximal singular operators in the introduced spaces.
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