TY - JOUR
T1 - A Hardy–Littlewood Maximal Operator for the Generalized Fourier Transform on R
AU - Ben Saïd, Salem
AU - Deleaval, Luc
N1 - Funding Information:
SBS is thankful to UAEU for the Start-up Grant No. 31S375.
Publisher Copyright:
© 2019, Mathematica Josephina, Inc.
PY - 2020/4/1
Y1 - 2020/4/1
N2 - In this paper, we define and study a canonical Hardy–Littlewood-type maximal operator associated with the one-dimensional generalized Fourier transform. For this operator to which covering methods do not apply, we construct a geometric maximal operator, which controls pointwise the canonical maximal operator, and for which we can use the machinery of real analysis to obtain a maximal theorem.
AB - In this paper, we define and study a canonical Hardy–Littlewood-type maximal operator associated with the one-dimensional generalized Fourier transform. For this operator to which covering methods do not apply, we construct a geometric maximal operator, which controls pointwise the canonical maximal operator, and for which we can use the machinery of real analysis to obtain a maximal theorem.
KW - Generalized Fourier transform
KW - Hardy–Littlewood maximal theorem
KW - Maximal function
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U2 - 10.1007/s12220-019-00183-6
DO - 10.1007/s12220-019-00183-6
M3 - Article
AN - SCOPUS:85073793790
SN - 1050-6926
VL - 30
SP - 2273
EP - 2289
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 2
ER -