Advanced Studies: Euro-Tbilisi Mathematical Journal

Lipschitz spaces under fractional convolution

E. Toksoy

We describe a generalization of Lipschitz spaces under fractional convolution and discuss some basic properties of these spaces. The aim of this work is to introduce and study a linear space A_p^{lip_(α,1)^β} (ℝ^d) of functions h belonging to Lipschitz space under fractional convolution whose fractional Fourier transforms 𝘍_βh belongs to Lebesgue spaces. We show that this space becomes a Banach algebra with the sum norm ∥h∥_{lip_(α,1)^β,p}=∥h∥ _{(α,1)_β} + ∥𝘍_β h∥_p and Θ (fractional convolution) convolution operation. Also we indicate that this space becomes an essential Banach module over L¹(ℝ^d) with Θ convolution.


Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 16(4) (2023), pp. 39-56