Product kernels adapted to curves in the space

Details Product kernels adapted to curves in the space Product kernels adapted to curves in the space

2009-05-24

arxiv.org/abs/0905.3889v1

Mathematics

Functional Analysis

31 pages

Scientific paper

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 sigularities 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.

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