Annals of Functional Analysis最新文献

In this paper, we introduce (weak) local and global Dunkl–Morrey-type spaces and investigate some properties of these spaces, such as embedding theorem, pre-dual spaces and norm-equivalence relationships with Herz-type spaces. The necessary and sufficient conditions for the boundedness of Dunkl-fractional-type maximal operators on these spaces are obtained. Moreover, a characterization of the Hardy local Dunkl–Morrey-type space and a block decomposition of local Dunkl–Morrey type spaces are established.

We investigate the Cauchy problem for a heat equation involving a fractional harmonic oscillator and an exponential nonlinearity:

where (varrho ge 0,~beta >0) and (f:{mathbb {R}}rightarrow {mathbb {R}}) exhibits exponential growth at infinity, with (f(0)=0.) We establish local well-posedness within the appropriate Orlicz spaces. Through the examination of small initial data in suitable Orlicz spaces, we obtain the existence of global weak-mild solutions. Additionally, precise decay estimates are presented for large time, indicating that the decay rate is influenced by the nonlinearity’s behavior near the origin. Moreover, we highlight that the existence of local nonnegative classical solutions is no longer guaranteed when certain nonnegative initial data are considered within the appropriate Orlicz space.

If a tuple of bounded operators have a common reducing subspace of finite dimension, its projective joint spectrum has an algebraic component. In general, the converse is not true and there might be algebraic components in the projective joint spectrum without corresponding common reducing subspaces. In this paper, we give necessary and sufficient conditions for the occurrence of such correspondence.

Starting from a fixed measure space ((X, {mathcal {F}}, mu )), with (mu ) a positive sigma-finite measure defined on the sigma-algebra ({mathcal {F}}), we continue here our study of a generalization (W^{(mu )}) of Brownian motion, and introduce a corresponding white-noise process. In detail, the generalized Brownian motion is a centered Gaussian process (W^{(mu )}), indexed by the elements A in ({mathcal {F}}) of finite (mu ) measure, and with covariance function (mu (Acap B)). The purpose of our present paper is to make precise and study the corresponding white-noise process, i.e., a point-wise process which is indexed by X, and which arises as a generalized (mu ) derivative of (W^{(mu )}). A key tool in our definition and analysis of this pair is a construction of three operators between the underlying Hilbert spaces. One of these operators is a stochastic integral, the second is a gradient associated with the measure (mu ), and the third is a mathematical expectation in the underlying probability space. We show that, with the setting of families of processes indexed by sets of measures (mu ), our results lead to new stochastic bundles. They serve in turn to extend the tool set for stochastic calculus.

In this paper, criteria for strong U-points and H-property in Orlicz sequence spaces equipped with the p-Amemiya norm ((1< p<infty )) are given. Next, compactly locally uniform rotundity and locally uniform rotundity of these spaces are deduced. Obtained results broaden the knowledge about these notions in Orlicz sequence spaces equipped with the p-Amemiya norm.

The paper is devoted to studies on exact and approximate smoothness in normed linear spaces. In particular, we develop the concept of approximate smoothness and present some of its new properties and characterizations. We pay a special attention to spaces of linear bounded operators on Banach and Hilbert spaces.

We use a cohomology theory coming from the canonical trace on a (C^*)-algebra of the projective variety to prove an analog of the Riemann Hypothesis for the Kuga–Sato varieties.

We provide compact imbedding results for Musielak–Sobolev spaces built on smooth bounded domains from Musielak functions, on which we impose, among others, natural integral conditions that extend those used in the framework of Orlicz spaces. We obtain the Rellich–Kondrachov theorem for regular Musielak functions. We then apply the results obtained to get a Poincaré-type inequality in Musielak spaces, which we use to solve a class of nonlinear elliptic problems.

Involutive L-algebras are introduced as a class of L-algebras X which embed into a factor group G of their structure group, so that X generates G and coincides with the set of involutions of G. A particular case exists for every group generated by involutions. In previous work it was shown that the projection lattice of a von Neumann algebra is an L-algebra which is determined, up to isomorphism, by the structure group of this L-algebra. Extending this result, an involutive L-algebra is associated to any von Neumann algebra as a complete invariant. In particular, it is proved that involutive L-algebras admit a self-action by involutive automorphisms which canonically extends to a self-action of the structure group. Several examples are considered, including those which give rise to non-degenerate involutive solutions to the set-theoretic Yang–Baxter equation.

In this paper, we characterize the strong continuity of composition semigroups on analytic Besov spaces (B_{p}(1<p<infty ).) First, we show that every semigroup of composition operators ({C_{varphi _{t}}}) are strongly continuous on (B_{p}(2le p<infty ).) However, we can find a semigroup ({varphi _t}) such that the induced composition operator (C_{varphi _t}) is not even bounded on (B_p(1<p<2).) We contribute novel counterexamples grounded in the geometric properties of the image domain of Kœnigs function to illustrate this point. Moreover, we provide a sufficient condition ensuring the strong continuity of any semigroup of composition operators in (B_{p}(1<p<infty ).) Additionally, we establish that ({C_{varphi _{t}}}) is not uniformly continuous on (B_{p}(1<p<infty ),) unless ({varphi _{t}}) is trivial.