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In this note we consider the parametric Marcinkiewicz integrals with mixed homogeneity along polynomials compound curves. Under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction, the Lp bounds of such operators are given by an extrapolation argument. Some previous results are greatly extended and improved.
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참고문헌 (28)
참고문헌 신청
A. Al-Salman / 2002 / Lp bounds for the function of Marcinkiewicz / Math. Res. Lett 9 (5-6) : 697 ~ 700
A. Al-Salman / 2010 / A note on parabolic Marcinkiewicz integrals along surfaces / Proc. A. Razmadze Math. Inst 154 : 21 ~ 36
A. Al-Salman / 2011 / On the L2 boundedness of parametric Marcinkiewicz integral operator / J. Math. Anal. Appl 375 (2) : 745 ~ 752
A. P. Calder´on / 1975 / Parabolic maximal functions associated with a dis-tribution / Adv. in Math 16 : 1 ~ 64
D. Fan / 1997 / Singular integral operators with rough kernels supported by subva-rieties / Amer. J. Math 119 (4) : 799 ~ 839
A. Al-Salman / 2010 / A note on parabolic Marcinkiewicz integrals along surfaces / Proc. A. Razmadze Math. Inst 154 : 21 ~ 36
A. Al-Salman / 2011 / On the L2 boundedness of parametric Marcinkiewicz integral operator / J. Math. Anal. Appl 375 (2) : 745 ~ 752
A. P. Calder´on / 1975 / Parabolic maximal functions associated with a dis-tribution / Adv. in Math 16 : 1 ~ 64
D. Fan / 1997 / Singular integral operators with rough kernels supported by subva-rieties / Amer. J. Math 119 (4) : 799 ~ 839
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