In a previous paper two of the authors introduced and study Gaussian Besov-Lipschitz spaces $B_{ p,q}^{ \alpha}(\gamma_{ d})$ and Gaussian Triebel-Lizorkin spaces $F_{ p,q}^{ \alpha}(\gamma_{ d})$. Now, in this paper we introduce the variable Gaussian Besov-Lipschitz spaces $B_{ p(\cdot),q(\cdot)}^{ \alpha}(\gamma_{ d})$ and the variable Gaussian Triebel-Lizorkin spaces $F_{ p(\cdot),q(\cdot)}^{ \alpha}(\gamma_{ d}),$ that is to say, Gaussian Besov-Lipschitz and Triebel-Lizorkin spaces with variable exponents, under certain additional regularity conditions on the exponents $p(\cdot)$ and $q(\cdot)$ introduced by Dalmasso and Scotto. Trivially, they include the Gaussian Besov-Lipschitz spaces $B_{ p,q}^{ \alpha}(\gamma_{ d})$ and Gaussian Triebel-Lizorkin spaces $F_{ p,q}^{ \alpha}(\gamma_{ d})$. We consider some inclusion relations of those spaces and finally we also prove some interpolation results for them.
Categories: math.CA