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We introduce a decoupling method on the Wiener space to define a wide classof an\-iso\-tro\-pic Besov spaces. The decoupling method is based on a generaldistributional approach and not restricted to the Wiener space.  The class of Besov spaces we introduce contains the traditional isotropicBesov spaces obtained by the real interpolation method, but also new spacesthat are designed to investigate backwards stochastic differential equations(BSDEs). As examples we discuss the Besov regularity (in the sense of ourspaces) of forward diffusions and local times. It is shown that among our newlyintroduced Besov spaces there are spaces that characterize quantitativeproperties of directional derivatives in the Malliavin sense without computingor accessing these Malliavin derivatives explicitly.  Regarding BSDEs, we deduce regularity properties of the solution processesfrom the Besov regularity of the initial data, in particular upper bounds fortheir $L_p$-variation, where the generator might be of quadratic type and whereno structural assumptions, for example in terms of a forward diffusion, areassumed. As an example we treat sub-quadratic BSDEs with unbounded terminalconditions.  Among other tools, we use methods from harmonic analysis. As a by-product, weimprove the asymptotic behaviour of the multiplicative constant in ageneralized Fefferman inequality and verify the optimality of the bound weestablished.

Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs