Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 32, No. 2, pp. 313-325 (2016)

Variable Lebesgue spaces and continuous wavelet transforms

Kristóf Szarvas

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

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