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

Authors:
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