We prove mixed-norm space-time estimates for solutions of the Schrödinger equation, with initial data in L-Sobolev or Besov spaces, and clarify the relation with adjoint restriction. RÉSUMÉ. Nous obtenons des estimations en norme-mixte espace-temps pour l’équation de Schrödinger avec valeurs initiales dans des espaces de Sobolev ou de Besov. Nous éclaircissons également leurs relations avec cel...

It is well known that functions in the analytic Besov space B1 on the unit disk D admits an integral representation f(z) = ∫ D z − w 1− zw dμ(w), where μ is a complex Borel measure with |μ|(D) < ∞. We generalize this result to all Besov spaces Bp with 0 < p ≤ 1 and all Lipschitz spaces Λt with t > 1. We also obtain a version for Bergman and Fock spaces.

Let G be a locally compact Vilenkin group. In this paper the characterizations of the Herz-type Besov space on G are obtained. And some properties of this space are discussed.

We prove the global well-posedness of the critical dissipative quasi-geostrophic equation for large initial data belonging to the critical Besov space Ḃ ∞,1(R ).

The concept of local growth envelope (ELGA, u) of the quasi-normed function space A is applied to the Besov spaces of generalized smoothness B p,q (Rn).

The characterization by weighted Lipschitz continuity is given for the Bloch space on the unit ball of Rn. Similar results are obtained for little Bloch and Besov spaces.