Abstract
Abstract—The motivation of this dissertation mainly is which affine frame wavelet systems span Lebesgue spaces have been investigated less. The technique we used is analogous to technique of Calderon-Zygmund operators, but we rely on Calderon-Zygmund decomposition theorem. We prove our main results without smoothness assumption on frame wavelets. We prove that affine tight frame wavelets span Lebesgue spaces under the condition, we also show that the affine tight frame operator extends from 2 () L to a bounded, linear and bijective operator on () p L , for 1. p Under such condition, the
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