The S-Transform on Hardy Spaces and Its Duals

Article Sidebar

PDF
Cite as:
Sunil Kumar Singh, Baby Kalita, The S-Transform on Hardy Spaces and Its Duals, Int. J. Anal. Appl., 7 (2) (2015), 171-178.

Main Article Content

Sunil Kumar Singh, Baby Kalita

Abstract

In this paper, continuity and boundedness results for the continuous S-transform in BMO and Hardy spaces are obtained. Furthermore, the continuous S-transform is also studied on the weighted BMO$_k$ and weighted Hardy spaces associated with a tempered weight function which was proposed by L. H\"ormander in the study of the theory of partial differential equations.

Article Details

References

  1. Chuong. N. M. and Duong. D. V., Boundedness of the wavelet integral operator on weighted function spaces, Russian Journal of Mathematical Physics, 20(3) (2013), 268-275.
  2. H ¨ormander. L., The Analysis of Linear Partial Differential Operators II, Springer-Verlag, Berlin Heidelberg New York, 1983.
  3. John. F. and Nirenberg. L., On functions of bounded mean oscillation , Communications on Pure and Applied Mathematics, 14 (1961), 415-426.
  4. Pathak. R. S. and Singh. S. K., Boundedness of the wavelet transform in certain function spaces, Journal of inequalities in pure and applied mathematics, 8(1) (2007), Article 23, 8 pages.
  5. Singh. S. K., The S-transform on spaces of type S, Integral Transforms and Special Functions, 23(7) (2012), 481-494.
  6. Singh. S. K., The S-transform on spaces of type W, Integral Transforms and Special Functions, 23(12) (2012), 891-899.
  7. Singh. S. K., The fractional S-transform of tempered ultradistibutions, Investigations in Mathematical Sciences, 2(2) (2012), 315-325.
  8. Singh. S. K., The fractional S-transform on spaces of type S, Journal of Mathematics, 2013 (2013), Article ID 105848.
  9. Singh. S. K., The fractional S-transform on spaces of type W, Journal of Pseudo-Differential Operators and Applications, 4(2) (2013), 251-265.
  10. Singh. S. K., A new integral transform: Theory part, Investigations in Mathematical Sciences, 3(1) (2013), 135-139.
  11. Singh. S. K., The S-Transform of distributions, The scientific world journal, 2014 (2014), Article ID 623294.
  12. Stockwell. R. G., Mansinha. L. and Lowe. R. P., Localization of the complex spectrum: The S transform, IEEE Trans. Signal Process., 44(4) (1996), 998-1001.
  13. Ventosa. S., Simon. C., Schimmel. M. , DaËœnobeitia. J. and M`anuel. A., The S-transform from a wavelet point of view, IEEE Trans. Signal Process., 56(07) (2008), 2771-2780.