On the operators related to C.W.T on general homogeneous spaces

Abstract

For homogeneous space G/H equipped with strongly quasi invariant measure $\nu$, we introduce the two-wavelet constant for square integrable representations and the orthogonal subspaces of $L^{2}(G/H)$, which are related to continuous wavelet transform (C.W.T). For admissible wavelet $\eta$ and $\Theta \in L^{p}(G/H);$ $1\leqslant p \leqslant \infty$, the localization operator $\Upsilon _{\Theta ,\eta }$ is introduced. The boundedness properties of localization operator is studied and it is shown that $\Upsilon _{\Theta ,\eta }$ is in Schatten p-class.