TY - JOUR
T1 - Norm inequalities for maximal operators
AU - Ben Said, Salem
AU - Negzaoui, Selma
N1 - Funding Information:
SBS would like to thankfully acknowledge the financial support awarded by UAEU through the UPAR grant No. 12S002.
Publisher Copyright:
© 2022, The Author(s).
PY - 2022
Y1 - 2022
N2 - In this paper, we introduce a family of one-dimensional maximal operators Mκ,m, κ≥ 0 and m∈ N∖ { 0 } , which includes the Hardy–Littlewood maximal operator as a special case (κ= 0 , m= 1). We establish the weak type (1 , 1) and the strong type (p, p) inequalities for Mκ,m, p> 1. To do so, we prove a technical covering lemma for a finite collection of intervals.
AB - In this paper, we introduce a family of one-dimensional maximal operators Mκ,m, κ≥ 0 and m∈ N∖ { 0 } , which includes the Hardy–Littlewood maximal operator as a special case (κ= 0 , m= 1). We establish the weak type (1 , 1) and the strong type (p, p) inequalities for Mκ,m, p> 1. To do so, we prove a technical covering lemma for a finite collection of intervals.
KW - Covering lemma
KW - Generalized Fourier transform
KW - Maximal operators
KW - Weak and strong type inequalities
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U2 - 10.1186/s13660-022-02874-1
DO - 10.1186/s13660-022-02874-1
M3 - Article
AN - SCOPUS:85140832653
SN - 1025-5834
VL - 2022
JO - Journal of Inequalities and Applications
JF - Journal of Inequalities and Applications
IS - 1
M1 - 134
ER -