We study Toeplitz operators between the pluriharmonic Bergman spaces for positive symbols on the ball. We give characterizations of bounded and compact Toeplitz operators taking a pluriharmonic Bergman space $b^p$ into another $b^q$ for $1<p,q<\infty$ in terms of certain Carleson and vanishing Carleson measures.

Suppose $E$ is an ordered locally convex space, $X_1$ and $X_2$ Hausdorff completely regular spaces and $Q$ a uniformly bounded, convex and closed subset of $M_t^{+}(X_1\times X_2,E)$. For $i=1,2$, let ${\mu }_i\in M_t^{+}(X_i,E)$. Then, under some topological and order conditions on $E$, necessary and sufficient conditions are established for the existence of an element in $Q$, having marginals ${\mu }_1$ and ${\mu }_2$.

Let w be a non-negative measurable function defined on the positive semi-axis and satisfying the reverse Hölder inequality with exponents 0 < α < β. In the present paper, sharp estimates of the compositions of the power means ${}_{\alpha }w\left(x\right):={\left((1/x){\int }_0^x{w}^{\alpha }\left(t\right)dt\right)}^{1/\alpha }$, x > 0, are obtained for various exponents α. As a result, for the function w a property of self-improvement of summability exponents is established.

We present definitions of Banach spaces predual to Campanato spaces and Sobolev-Campanato spaces, respectively, and we announce some results on embeddings and isomorphisms between these spaces. Detailed proofs will appear in our paper in Math. Nachr.

For $U$ a balanced open subset of a Fréchet space $E$ and $F$ a dual-Banach space we introduce the topology ${\tau }_{\gamma }$ on the space $\mathscr{H}(U,F)$ of holomorphic functions from $U$ into $F$. This topology allows us to construct a predual for $(\mathscr{H}(U,F),{\tau }_{\delta })$ which in turn allows us to investigate the topological structure of spaces of vector-valued holomorphic functions. In particular, we are able to give necessary and sufficient conditions for the equivalence and compatibility of various topologies on spaces of vector-valued holomorphic functions....

This note brings a complement to the study of genericity of functions which are nowhere analytic mainly in a measure-theoretic sense. We extend this study to Gevrey classes of functions.

On s’intéresse à la résolution du système de Navier-Stokes incompressible à densité variable dans le demi-espace ${ℝ}_{+}^n:={ℝ}^{n-1}\times ]0,\infty [$ en dimension $n\ge 3.$ On considère des données initiales à régularité critique. On établit que si la densité initiale est proche d’une constante strictement positive dans $L^{\infty }\cap {\dot{W}}^{1,n}$ et si la vitesse initiale est petite par rapport à la viscosité dans l’espace de Besov homogène ${\dot{B}}_{n,1}^0$ alors le système de Navier-Stokes admet une unique solution globale. La démonstration repose sur de nouvelles estimations...