Isomorphism of some anisotropic Besov and sequence spaces

Convergence in law for certain additive functionals of symmetric stable processes under strong topology

“…We will consider a separable Banach subspace of Lip p (δ, β) defined by: , 1) , i = 1, 2 as t → 0; and ω p (f, t 1 , t 2 ) = o ω δ β (t 1 , t 2 ) as t 1 ∧ t 2 → 0 . For detailed discussion on anisotropic Besov spaces see Kamont [8,9].…”

Continuity in law with respect to the Hurst index of some additive functionals of sub-fractional Brownian motion

“…Now, for any continuous functions f on I 2 , we have the following decomposition f (t, .)). We have the following characterization of anisotropic Besov spaces in terms of the coefficients of the expansion of a continuous function with respect to a basis which consists of tensor products of Schauder functions, and we refer to [15,Theorem A.2]. This characterization was used by Ouahhabi and Sghir [21,Theorem 3.3], to prove some regularities of the generalized fractional derivative of local time of α-symmetric stable process with 1 < α ≤ 2, in some anisotropic Besov spaces.…”

Weak convergence to fractional Brownian motion in some anisotropic Besov space

“…The first characterisation of these spaces in the L p -norm with p < ∞ by coefficients in the Faber-Schauder basis have been done in Ciesielski et al [3]. The multiparameter case have been considered recently by Kamont [6] and [7]. To prove our main results, we need the characterization of the Besov spaces in terms of the coefficients of the expansion of a continuous function in the basis consisting of tensor products of Faber-Schauder functions.…”

“…The first characterization of these spaces, in the L p -norm with p < +∞, by coefficients in the Faber-Schauder basis has been established in Ciesielski et al [3]. The multiparameter case was considered by Kamont [6] et [7].…”