Convergence and Characterization of Wavelets Associated with Dilation Matrix in VariableLpSpaces

摘要

We study the convergence of wavelet expansions associated with dilation matrix in the variableLp(·)(ℝd)spaces using the approximate identity. Also, we obtain conditions for the wavelet characterizations ofLp(·)(ℝd)with respect to norm estimates. Moreover, the results of Izuki (2008) and Kumar (2009) have been extended.