JournalsrmiVol. 27, No. 3pp. 1023–1057

Product kernels adapted to curves in the space

  • Valentina Casarino

    Università degli Studi di Padova, Vicenza, Italy
  • Paolo Ciatti

    Università degli Studi di Padova, Italy
  • Silvia Secco

    Padova, Italy
Product kernels adapted to curves in the space cover
Download PDF

Abstract

We establish LpL^p-boundedness for a class of operators that are given by convolution with product kernels adapted to curves in the space. The LpL^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 LpL^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 LpLqL^p-L^q estimates for analytic families of fractional operators along curves in the space.

Cite this article

Valentina Casarino, Paolo Ciatti, Silvia Secco, Product kernels adapted to curves in the space. Rev. Mat. Iberoam. 27 (2011), no. 3, pp. 1023–1057

DOI 10.4171/RMI/662