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<p>In this article, the generalized continuous wavelet transform (GCWT) in <i>n</i>-dimensions is introduced, and its Parseval type identity and reconstruction formula are obtained. A novel convolution associated with GCWT is proposed, and its bounds are established. Furthermore, the continuity and boundedness results for GCWT on weighted bounded mean oscillation (BMO) and weighted Hardy space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H^{p}_{k}\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>H</mi> <mi>k</mi> <mi>p</mi> </msubsup> </math></EquationSource> </InlineEquation> spaces are investigated.</p>

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The generalized continuous wavelet transform on BMO and Hardy spaces

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • Awniya Kumar,
  • Sunil Kumar Singh,
  • Jyoti Kumari,
  • Shweta

摘要

In this article, the generalized continuous wavelet transform (GCWT) in n-dimensions is introduced, and its Parseval type identity and reconstruction formula are obtained. A novel convolution associated with GCWT is proposed, and its bounds are established. Furthermore, the continuity and boundedness results for GCWT on weighted bounded mean oscillation (BMO) and weighted Hardy space \(H^{p}_{k}\) H k p spaces are investigated.