Eötvös Loránd University
Abstract: In this paper we summarize the previous results in the topic of variable Lebesgue space. We present the basic properties of the variable Lebesgue spaces and investigate norm and almost everywhere convergence of the inverse continuous wavelet transform in the variable Lebesgue space.
Keywords: Variable Lebesgue spaces, continuous wavelet transform, Wiener amalgam spaces, $\theta$-summability, inversion formula.
Classification (MSC2000): 42C40; 42C15, 42B08, 42A38, 46B15
Full text of the article: