Variable exponent Besov-Lipschitz and Triebel-Lizorkin spaces for the Gaussian measure.

In this paper, we introduce variable Gaussian Besov-Lipschitz Bα _p(p);q(γ)(d) and Triebel-Lizorkin spaces Fα p(γ);q(γ)(d); i.e., Gaussian Besov-Lipschitz and Triebel-Lizorkin spaces with variable exponents p(γ) and q(γ), under certain regularity conditions on the functions p(γ) and q(γ). The condition on p(γ) is associated with the Gaussian measure and was introduced in [3]. Trivially, they include the Gaussian Besov-Lipschitz Bα p;q(d) and Triebel-Lizorkin spaces Fα p;q(d) for p; q constants, which were introduced and studied in [10]. We consider some inclusion relations of those spaces and finally prove some interpolation results for them. [ABSTRACT FROM AUTHOR]