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Pseudodifferential operators on weighted Hardy spaces. (English) Zbl 1442.47035

Summary: We study two sufficient conditions for the boundedness of a class of pseudodifferential operators \(T\) with symbols in the Hörmander class \(S_{\rho,\delta}^m (\mathbb{R}^n)\) on weighted Hardy spaces \(H_\omega^1 (\mathbb{R}^n)\), where \(\omega\) belongs to Muckenhoupt class \(A_p\). The first one is an estimate from \(H_\omega^1 (\mathbb{R}^n)\) into \(L_\omega^1 (\mathbb{R}^n)\). We get a better range of admissible \(p\) and \(m\). The second one is a weighted version bounded for the operators \(T\) on \(H_\omega^1(\mathbb{R}^n)\), and it is an addition to the literature.

MSC:

47G30 Pseudodifferential operators
35S05 Pseudodifferential operators as generalizations of partial differential operators
42B30 \(H^p\)-spaces
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