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September, 2011 Product kernels adapted to curves in the space
Valentina Casarino , Paolo Ciatti , Silvia Secco
Rev. Mat. Iberoamericana 27(3): 1023-1057 (September, 2011).

Abstract

We establish $L^p$-boundedness for a class of operators that are given by convolution with product kernels adapted to curves in the space. The $L^p$ bounds follow from the decomposition of the adapted kernel into a sum of two kernels with singularities concentrated respectively on a coordinate plane and along the curve. The proof of the $L^p$-estimates for the two corresponding operators involves Fourier analysis techniques and some algebraic tools, namely the Bernstein-Sato polynomials. As an application, we show that these bounds can be exploited in the study of $L^p-L^q$ estimates for analytic families of fractional operators along curves in the space.

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Valentina Casarino . Paolo Ciatti . Silvia Secco . "Product kernels adapted to curves in the space." Rev. Mat. Iberoamericana 27 (3) 1023 - 1057, September, 2011.

Information

Published: September, 2011
First available in Project Euclid: 9 August 2011

zbMATH: 1236.42009
MathSciNet: MR2895343

Subjects:
Primary: 42B20 , 44A35

Keywords: $L^P$ estimates , Bernstein-Sato polynomials , convolution , product kernels

Rights: Copyright © 2011 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.27 • No. 3 • September, 2011
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