TY - JOUR
T1 - L p estimates of rough maximal functions along surfaces with applications
AU - Al-Salman, Ahmad
AU - Jarrah, Abdulla M.
PY - 2016/8/1
Y1 - 2016/8/1
N2 - In this paper, we study the Lp mapping properties of certain class of maximal oscillatory singular integral operators. We prove a general theorem for a class of maximal functions along surfaces. As a consequence of such theorem, we establish the Lp boundedness of various maximal oscillatory singular integrals provided that their kernels belong to the natural space Llog L(Sn−1). Moreover, we highlight some additional results concerning operators with kernels in certain block spaces. The results in this paper substantially improve previously known results.
AB - In this paper, we study the Lp mapping properties of certain class of maximal oscillatory singular integral operators. We prove a general theorem for a class of maximal functions along surfaces. As a consequence of such theorem, we establish the Lp boundedness of various maximal oscillatory singular integrals provided that their kernels belong to the natural space Llog L(Sn−1). Moreover, we highlight some additional results concerning operators with kernels in certain block spaces. The results in this paper substantially improve previously known results.
KW - highly monotone curves
KW - maximal functions
KW - Oscillatory singular integrals
KW - rough kernels
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U2 - 10.1007/s10114-016-5274-0
DO - 10.1007/s10114-016-5274-0
M3 - Article
AN - SCOPUS:84978081326
SN - 1439-8516
VL - 32
SP - 925
EP - 942
JO - Acta Mathematica Sinica, English Series
JF - Acta Mathematica Sinica, English Series
IS - 8
ER -