The Curvelet Transform on Function Spaces
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Authors: D. LHAMU, S. K. SINGH, A. KUMAR AND C. P. PANDEY
DOI: 10.46793/KgJMat2606.941L
Abstract:
In this paper, we delve into the comprehensive exploration of the continuous curvelet transform (CCT), an advanced iteration of the continuous wavelet transform. Renowned for its applications in diverse mathematical realms such as signal analysis, image processing, and seismic exploration, the CCT holds significant promise. Our focus is on an in-depth examination of the CCT’s properties within function spaces, i.e., in Sobolev spaces Hs(ℝ2), Wm,p(ℝ2), the weighted Sobolev space Wκm,p(ℝ2), the generalized Sobolev space Hwω(ℝ2), Besov space Bpα,q(ℝ2), weighted Besov space Bp,κα,q(ℝ2), Hardy space Hp(ℝ2) and BMO(ℝ2) space. Through investigation, we uncover valuable insights into the continuity and boundedness of the CCT within these function spaces.
Keywords:
Curvelet transform, Sobolev space, Besov space, Hardy space, BMO space.
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