Abstract
The wavelet transform is an useful mathematical tool. It is a mapping of a time signal to the time-scale joint representation. The wavelet transform is generated from a wavelet function by dilation and translation. This wavelet function satisfies an admissible condition so that the original signal can be reconstructed by the inverse wavelet transform. In this study, we firstly give some basic properties of the weighted variable exponent amalgam spaces. Then we investigate the convergence of the θ-means of f in these spaces under some conditions. Finally, using these results the convergence of the inverse continuous wavelet transform is considered in these spaces.
Highlights
The variable exponent Lebesgue line is the space (Lp)(:)(Rd) spaces and a class of nonlinear problems with variable exponential growth have been new and interesting topics
The wavelet transform is generated from a wavelet function by dilation and translation
This wavelet function satis...es an admissible condition so that the original signal can be reconstructed by the inverse wavelet transform
Summary
The variable exponent Lebesgue Lp(:)(Rd) spaces and a class of nonlinear problems with variable exponential growth have been new and interesting topics. Many di¤erent forms of amalgam spaces have been studied by some authors (see [25], [33], [24], [15] and [18]). Variable exponent amalgam spaces Lp(:); lq and some basic properties, such as Banach function space, Hölder type inequalities, interpolation, bilinear multipliers and the boundedness of maximal operator, have been investigated recently. Uribe and Fiorenza [10], Szarvas and Weisz [34] obtained similar results for the space Lp(:) Rd : In this study we will discuss the convergence of the inverse continuous wavelet transform in weighted variable exponent amalgam spaces. We obtain more general results with respect to [34]
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