Nonisotropic dilations and the method of rotations with weight

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.

Locations

• Proceedings of the American Mathematical Society - View - PDF
• Kanazawa University Repository for Academic Resources (DSpace) (Kanazawa University) - View - PDF