@article{Pineda2023, 
author = {Ebner Pineda and Luz Rodriguez and Wilfredo Urbina},
title = {Variable exponent Besov-Lipschitz and Triebel-Lizorkin spaces for the Gaussian measure},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {11},
pages = {27128-27150},
keywords = {Ornstein-Uhlenbeck, variable exponent, Besov-Lipschitz, Triebel-Lizorkin, Gaussian measure},
url = {https://www.sciopen.com/article/10.3934/math.20231388},
doi = {10.3934/math.20231388},
abstract = {In this paper, we introduce variable Gaussian Besov-Lipschitz        B          p      (      ⋅      )      ,      q      (      ⋅      )              α        (      γ          d        ) and Triebel-Lizorkin spaces        F          p      (      ⋅      )      ,      q      (      ⋅      )              α        (      γ          d        )  , i.e., Gaussian Besov-Lipschitz and Triebel-Lizorkin spaces with variable exponents    p  (  ⋅  ) and    q  (  ⋅  ), under certain regularity conditions on the functions    p  (  ⋅  ) and    q  (  ⋅  ). The condition on    p  (  ⋅  ) is associated with the Gaussian measure and was introduced in [3]. Trivially, they include the Gaussian Besov-Lipschitz        B          p      ,      q              α        (      γ          d        ) and Triebel-Lizorkin spaces        F          p      ,      q              α        (      γ          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.}
}