If Tμ is a Fourier multiplier such that μ is any (possibly unbounded) symbol with uniformly bounded q-variation on dyadic coronas, we prove that the commutator [T, Tμ] = TTμ−TμT is bounded on the Besov space B p (R ), if T is any bounded linear operator on a couple of Besov spaces Bj ,rj p (R) (j = 0, 1, and 0 < σ1 < σ < σ0).

In this paper, we obtain a refinement of the Young theorem. The Young theorem tells us that the Fourier transform F sends the L functions to the Lp functions, if 1 ≤ p ≤ 2. This theorem has a refinement. For example, F : L → B ∞1, where B pq is the Besov space. In this present paper we shall consider the more refined version of this theorem by using the amalgams and the Besov spaces.

In a celebrated construction, Chen and Skriganov gave explicit examples of point sets achieving the best possible L2-norm of the discrepancy function. We consider the discrepancy function of the ChenSkriganov point sets in Besov spaces with dominating mixed smoothness and show that they also achieve the best possible rate in this setting. The proof uses a b-adic generalization of the Haar syste...

The aim of this paper is to characterize compactly supported re-nable distributions in Triebel-Lizorkin spaces and Besov spaces by projection operators on certain wavelet space and by some operators on a nitely dimensional space.

The problem of density estimation on R is concerned. Adopting the maxiset point of view, the aim of this paper is threefold. Firstly, we prove that the maxiset of any elitist rule is contained in the intersection of a Besov space and a weak Besov space. Secondly, we provide an adaptive procedure for which the maxiset is the largest one among elitist rules (ideal maxiset). Thirdly, we point out ...

We give various equivalent formulations to the (partially) open problem about Lboundedness of Bergman projections in tubes over cones. Namely, we show that such boundedness is equivalent to the duality identity between Bergman spaces, A ′ = (Ap)∗, and also to a Hardy type inequality related to the wave operator. We introduce analytic Besov spaces in tubes over cones, for which such Hardy inequa...

Abstract. We consider a Korteweg-de Vries equation perturbed by a noise term on a bounded interval with periodic boundary conditions. The noise is additive, white in time and “almost white in space”. We get a local existence and uniqueness result for the solutions of this equation. In order to obtain the result, we use the precise regularity of the Brownian motion in Besov spaces, and the metho...