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Oscillatory kernels in certain Hardy-type spaces. (English) Zbl 0813.42012
This paper continues work by one of the authors on oscillating integrals on Besov spaces [cf. D. Fan, J. Math. Anal. Appl. 187, No. 3, 986- 1002 (1994; preceding review)]. In the present paper the authors consider oscillating integrals on the spaces \(H^ p_ 0(\mathbb{R}^ n)\), \(p\leq 1\). Their results extend the result by Fan, which corresponds to the case \(p= 1\).

MSC:
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B30 \(H^p\)-spaces
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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