We consider a class of Nemytskii superposition operators that covers the nonlinear part of traveling wave models from laser dynamics, population dynamics, and chemical kinetics. Our main result is the -continuity property of these operators over Sobolev-type spaces of periodic functions.
On montre que les fonctions qui opèrent, par composition a gauche, sur l’espace de Besov d’exposant , avec , dans l’espace euclidien de dimension , sont précisément les fonctions lipschitziennes.
In this paper we use the Calderón-Zygmund operator theory to prove a Calderón type reproducing formula associated with a para-accretive function. Using our Calderón-type reproducing formula we introduce a new class of the Besov and Triebel-Lizorkin spaces and prove a Tb theorem for these new spaces.
In this article a general result on smooth truncation of Riesz and Bessel potentials in Orlicz-Sobolev spaces is given and a capacitary type estimate is presented. We construct also a space of quasicontinuous functions and an alternative characterization of this space and a description of its dual are established. For the Riesz kernel Rm, we prove that operators of strong type (A, A), are also of capacitaries strong and weak types (m,A).
On étudie les espaces de Sobolev construits sur un espace localement convexe muni d’une mesure gaussienne centree . Si est de Radon, on démontre que les capacités naturelles sont tendues sur les compacts. Cela résulte d’un principe général relatif aux quasi-normes.On s’intéresse également aux fonctions quasi-continues a valeurs banachiques, ce qui est utile pour les propriétés de Nikodym, et à des applications à la continuité des trajectoires des intégrales stochastiques.
In the previous papers concerning the change of variables formula (in the form involving the Banach indicatrix) various assumptions were made about the corresponding transformation (see e.g. [BI], [GR], [F], [RR]). The full treatment of the case of continuous transformation is given in [RR]. In [BI] the transformation was assumed to be continuous, a.e. differentiable and with locally integrable Jacobian. In this paper we show that none of these assumptions is necessary (Theorem 2). We only need...
We characterize those anisotropic Sobolev spaces on tori in the and uniform norms for which the idempotent multipliers have a description in terms of the coset ring of the dual group. These results are deduced from more general theorems concerning invariant projections on vector-valued function spaces on tori. This paper is a continuation of the author’s earlier paper [W].