Pseudodifferential Operators on Weighted Hardy Spaces. (11th March 2020) - Deng, Yu-long; Long, Shun-chao
Abstract : We study two sufficient conditions for the boundedness of a class of pseudodifferential operators T with symbols in the Hölmander class S ρ, δ m ℝ n on weighted Hardy spaces H ω 1 ℝ n, where ω belongs to Muckenhoupt class A p . The first one is an estimate from H ω 1 ℝ n into L ω 1 ℝ n . We get a better range of admissible p and m . The second one is a weighted version bounded for the operators T on H ω 1 ℝ n, and it is an addition to the literature.