平特五不中

Rough singular integrals: A1 theory.

听In this mostly expository talk we will discuss new results for rough Singular Integral Operators involving $A_1$ weights. These are convolution operators whose kernels do not satisfy the standard regularity conditions (Lipschitz or Dini). Being more precise we will discuss estimates for these operators in the context of weighted $L^p$ spaces with weights satisfying the $A_1$ condition. These results are known since the 80's (work of Duoandikoetxea y Rubio de Francia) for $A_p$ weights but we found quantitative estimates in the context of the special class of $A_1$. Most probably these results are far from satisfactory and we will discuss some open problems. This is a joint work with I. Rivera-Rios and L. Roncal.

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