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We study two sufficient conditions for the boundedness of a class of pseudodifferential operators T with symbols in the Hölmander class Sρ,δmℝn on weighted Hardy spaces Hω1ℝn, where ω belongs to Muckenhoupt class Ap. The first one is an estimate from Hω1ℝn into Lω1ℝn. We get a better range of admissible p and m. The second one is a weighted version bounded for the operators T on Hω1ℝn, and it is an addition to the literature.doi:10.1155/2020/7154125 fatcat:u54t2grywncodapw44psvn4sau