Smoothing Properties of Bilinear Operators and Leibniz-Type Rules in Lebesgue and Mixed Lebesgue Spaces

摘要

We prove that bilinear fractional integral operators and similar multipliersare smoothing in the sense that they improve the regularity of functions. Wealso treat bilinear singular multiplier operators which preserve regularity andobtain several Leibniz-type rules in the contexts of Lebesgue and mixedLebesgue spaces.