TY - JOUR
T1 - L p Estimates of certain rough parametric Marcinkiewicz functions
AU - Hawawsheh, Laith
AU - Al-Salman, Ahmad
N1 - Publisher Copyright:
© 2019, Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/10/1
Y1 - 2019/10/1
N2 - We prove Lp estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the L1(Sn − 1) integrability condition. The obtained Lp estimates resolve a problem left open in previous work. Our argument is based on duality technique and direct estimation of operators. As a consequence of our result, we deduce the Lp boundedness of a class of fractional Marcinkiewicz integral operators.
AB - We prove Lp estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the L1(Sn − 1) integrability condition. The obtained Lp estimates resolve a problem left open in previous work. Our argument is based on duality technique and direct estimation of operators. As a consequence of our result, we deduce the Lp boundedness of a class of fractional Marcinkiewicz integral operators.
KW - Marcinkiewicz integrals
KW - Marcinkiewicz interpolation theorem
KW - parametric Marcinkiewicz functions
KW - rough kernels
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U2 - 10.1007/s11464-019-0792-6
DO - 10.1007/s11464-019-0792-6
M3 - Article
AN - SCOPUS:85074192534
SN - 1673-3452
VL - 14
SP - 867
EP - 879
JO - Frontiers of Mathematics in China
JF - Frontiers of Mathematics in China
IS - 5
ER -