Nonisotropic dilations and the method of rotations with weight

Sato, Shuichi

doi:10.1090/S0002-9939-2011-11188-2

Nonisotropic dilations and the method of rotations with weight
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Abstract:

We consider maximal functions $Mf(x,\theta )$, singular integrals $Hf(x,\theta )$, and maximal singular integrals $H_*f(x,\theta )$ on $\mathbb R^n\times S^{n-1}$ associated with homogeneous curves, for functions $f$ on $\mathbb R^n$. We prove certain weighted mixed norm estimates for them. These results are applied to the theory of singular integrals with variable kernels via the method of rotations of Calderón-Zygmund.

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