Two Extrapolation Theorems for Related Weights and Aplications

M.LORENTE, M.S. RIVEROS

Mathematical Inequalities and Applications

Lugar: Zagreb-Croatia; Año: 2006

In this paper we prove two extrapolation theorems  for related weights. The theorems  proved  by C. Segovia and J.L. Torrea in [C. Segovia and J.L. Torrea,  Weighted inequalities for commutators of fractional and singular integrals. Publ. Mat. 35  (1991)  209-235] are adapted for one-sided weights. We apply these extrapolation theorems to improve weighted inequalities for commutators (with symbol b depending on the related weights) of   several one-sided operators such as the Weyl and the Riemann-Liouville fractional integrals, or one-sided maximal operators given by the convolution with a smooth function.  We also characterize the symbols b for which the commutators of these one-sided operators are bounded.