Square-like Functions Generated by a Composite Wavelet Transform

Aliev I. A., Bayrakci S.

Mediterranean Journal of Mathematics, vol.8, no.4, pp.553-561, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 4
  • Publication Date: 2011
  • Doi Number: 10.1007/s00009-010-0084-6
  • Journal Name: Mediterranean Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.553-561
  • Keywords: Square functions, wavelet transform, Calderon reproducing formula, semigroup, convolution
  • Akdeniz University Affiliated: Yes

Abstract

The classical square functions play important role in Harmonic Analysis and have a very direct connection with L2-estimates and Littlewood-Paley theory. In this paper we introduce a new variant of square-like functions generated by some composite wavelet transform. We establish Calderón-type reproducing formula and then prove L2-boundedness of newly defined square-like functions. © 2010 Springer Basel AG.