TY - JOUR
T1 - Grand Lebesgue Spaces with Mixed Local and Global Aggrandization and the Maximal and Singular Operators
AU - Rafeiro, H.
AU - Samko, S.
AU - Umarkhadzhiev, S.
N1 - Publisher Copyright:
© 2023, Akadémiai Kiadó.
PY - 2023/12
Y1 - 2023/12
N2 - 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.
AB - 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.
KW - grand Lebesgue space
KW - maximal function
KW - maximal singular integral
KW - singular integral
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U2 - 10.1007/s10476-023-0243-1
DO - 10.1007/s10476-023-0243-1
M3 - Article
AN - SCOPUS:85175036770
SN - 0133-3852
VL - 49
SP - 1087
EP - 1106
JO - Analysis Mathematica
JF - Analysis Mathematica
IS - 4
ER -