  Using structures of Abstract Wiener Spaces, we define a fractional Brownian
field indexed by a product space $(0,1/2] \times L^2(T,m)$, $(T,m)$ a separable
measure space, where the first coordinate corresponds to the Hurst parameter of
fractional Brownian motion. This field encompasses a large class of existing
fractional Brownian processes, such as L\'evy fractional Brownian motions and
multiparameter fractional Brownian motions, and provides a setup for new ones.
We prove that it has satisfactory incremental variance in both coordinates and
derive certain continuity and H\"older regularity properties in relation with
metric entropy. Also, a sharp estimate of the small ball probabilities is
provided, generalizing a result on L\'evy fractional Brownian motion. Then, we
apply these general results to multiparameter and set-indexed processes,
proving the existence of processes with prescribed local H\"older regularity on
general indexing collections.
