Wavelet frame characterization of Lebesgue spaces on local fields
Received: 21.IX.2017, Revised: 7.II.2018, Accepted: 1.III.2018
Abstract. Shah and Debnath [Tight wavelet frames on local fields, Analysis, 33 (2013), 293-307] have derived an explicit method for constructing tight wavelet frames on local fields using the machinery of unitary extension principle. Continuing our investigation of wavelet frames on local fields, this paper deals with the establishment of complete characterization of functions in Lebesgue spaces $L^p(K), 1<p<\infty$, in terms of their wavelet frame coefficients.
Keywords: Wavelet frame, extension principle, Lebesgue space, maximal function, local field, Fourier transform
Mathematics Subject Classification (2010): 42C15; 42C40, 42B35, 43A70, 11S85
Firdous A. Shah, Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India
Shallu Sharma, Department of Mathematics, University of Jammu, Jammu-180006, Jammu and Kashmir, India
M. Younus Bhat, Department of Mathematics, National Institute of Technology, Srinagar-190006, Jammu and Kashmir, India