Regularity of Weighted Tensorized Fractional Brownian Fields and associated function spaces

We investigate a new class of self-similar fractional Brownian fields, called
Weighted Tensorized Fractional Brownian Fields (WTFBS). These fields,
introduced in the companion paper \cite{ELLV}, generalize the well-known
fractional Brownian sheet (FBs) by relaxing its tensor-product structure,
resulting in new self-similar Gaussian fields with stationary rectangular
increments that differ from the FBs. We analyze the local regularity properties
of these fields and introduce a new concept of regularity through the
definition of Weighted Tensorized Besov Spaces. These spaces combine aspects of
mixed dominating smoothness spaces and hyperbolic Besov spaces, which are
similar in structure to classical Besov spaces. We provide a detailed
characterization of these spaces using Littlewood-Paley theory and hyperbolic
wavelet analysis.