PARABOLIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO POLYNOMIALS COMPOUND CURVES AND EXTRAPOLATION

Title & Authors
PARABOLIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO POLYNOMIALS COMPOUND CURVES AND EXTRAPOLATION
Liu, Feng; Zhang, Daiqing;

Abstract
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 $\small{L^p}$ bounds of such operators are given by an extrapolation argument. Some previous results are greatly extended and improved.
Keywords
Marcinkiewicz integrals;rough kernels;mixed homogeneity;extrapolation;
Language
English
Cited by
1.
\$\$L^p\$\$ L p bounds for Marcinkiewicz integrals associated to homogeneous mappings, Monatshefte für Mathematik, 2016, 181, 4, 875
2.
BOUNDS FOR NONISOTROPIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES, Journal of the Australian Mathematical Society, 2015, 99, 03, 380
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