Abstract
Weighted Hardy spaces were first studied by Gacía-Cuerva [GC] for the case of weight functions in the A ∞ class. Generalization to the case of weight functions satisfying only the doubling condition was given by Strömberg and Torchinsky [ST]. Both of these works are concerned with the weighted Hardy spaces on ℝn. If we try to generalize the arguments of [GC] and [ST] so that we can deal with weighted Hardy spaces on a domain of ℝn, we meet with considerable technical difficulties since in those papers the convolution and the Fourier transform on ℝn are used as basic tools and the use of testing functions in the Schwartz class S seems to be unavoidable.
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References
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© 2000 Kluwer Academic Publishers
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Miyachi, A. (2000). Weighted Hardy Spaces on a Domain. In: Begehr, H.G.W., Gilbert, R.P., Kajiwara, J. (eds) Proceedings of the Second ISAAC Congress. International Society for Analysis, Applications and Computation, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0269-8_8
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DOI: https://doi.org/10.1007/978-1-4613-0269-8_8
Publisher Name: Springer, Boston, MA
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