On Function Spaces with Fractional Fourier Transform in Weighted Lebesgue Spaces

Abstract

Let w and ω be weight functions on (Formula presented.). In this work, we define (Formula presented.) to be the vector space of (Formula presented.) such that the fractional Fourier transform (Formula presented.) belongs to (Formula presented.) for (Formula presented.). We endow this space with the sum norm (Formula presented.) and show that (Formula presented.) becomes a Banach space and invariant under time-frequency shifts. Further we show that the mapping (Formula presented.) is continuous from (Formula presented.), the mapping (Formula presented.) is continuous from (Formula presented.) and (Formula presented.) is a Banach module over (Formula presented.) with Θ convolution operation. At the end of this work, we discuss inclusion properties of these spaces. © 2015, Toksoy and Sandıkçı; licensee Springer.