Stochastic integration with respect to fractional processes in Banach spaces

In the article, integration of temporal functions in (possibly non-UMD) Banach spaces with respect to non-Gaussian) fractional processes from a finite sum Wiener chaoses is treated. The family that considered includes, for example, Brownian motions any Hurst parameter or, more generally, fractionally filtered generalized Hermite processes. class includes large variety most commonly used function such as Lebesgue spaces, Sobolev Besov and Lizorkin-Triebel spaces. characterization domains integrals on both bounded unbounded intervals given scalar cylindrical general, integrand takes values space ?-radonifying operators certain homogeneous Sobolev-Slobodeckii into space. Moreover, an equivalent terms pointwise kernel also if isomorphic subspace cartesian product mixed results are subsequently applied stochastic convolution which necessary sufficient conditions measurability continuity found. As application, space-time solution parabolic equation order 2m distributed noise low time regularity shown well heat Neumann boundary higher regularity.