Let μ be a nonnegative Radon measure on R which only satisfies the following growth condition that there exists a positive constant C such that μ B x, r ≤ Cr for all x ∈ R, r > 0 and some fixed n ∈ 0, d . In this paper, the authors prove that for suitable indexes ρ and λ, the parametrized g∗ λ function M∗,ρ λ is bounded on L μ for p ∈ 2,∞ with the assumption that the kernel of the operator M∗,ρ...

The purpose of this note is to illustrate a construction technique which has proved useful, and apply it to solve an interesting problem. For a more complete discussion of the theory of bounded homomorphisms and lattices, see Chapter II of [3]. 1. Unbounded lattices We begin with a well known criterion for meet semidistributivity. If L is a finite lattice and a ∈ J(L), let κ(a) be the largest e...

We establish the following result. Theorem. Let α : G → L(X) be a σ(X, X∗) integrable bounded group representation whose Arveson spectrum Sp(α) is scattered. Then the subspace generated by all eigenvectors of the dual representation α∗ is w∗ dense in X∗. Moreover, the σ(X, X∗) closed subalgebra Wα generated by the operators αt (t ∈ G) is semisimple. If, in addition, X does not contain any copy ...

Let X be a metric space and define the category B(X) of manifolds bounded over X in the usual way [FW]. The objects of B(X) are manifolds M equipped with proper2 maps p : M → X. These maps p need not be continuous. A morphism (M1, p1) → (M2, p2) between objects of B(X) is a continuous map f : M1 →M2 which is bounded over X in the sense that there exists k > 0 for which d(p1(m), p2(f(m))) < k fo...

A family F of graphs is said to be (δ, χ)-bounded if there exists a function f(x) satisfying f(x) → ∞ as x → ∞, such that for any graph G from the family, one has f(δ(G)) ≤ χ(G), where δ(G) and χ(G) denotes the minimum degree and chromatic number of G, respectively. Also for any set {H1,H2, . . . ,Hk} of graphs by Forb(H1,H2, . . . ,Hk) we mean the class of graphs that contain no Hi as an induc...

‎let $x,y$ be normed spaces with $l(x,y)$ the space of continuous‎ ‎linear operators from $x$ into $y$‎. ‎if ${t_{j}}$ is a sequence in $l(x,y)$,‎ ‎the (bounded) multiplier space for the series $sum t_{j}$ is defined to be‎ [ ‎m^{infty}(sum t_{j})={{x_{j}}in l^{infty}(x):sum_{j=1}^{infty}%‎ ‎t_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $s:m^{infty}(sum t_{j})rightarrow y$ associat...

For any semifinite von Neumann algebra ${\mathcal M}$ and $1\leq p<\infty$, we introduce a natutal $S^1$-valued noncommutative $L^p$-space $L^p({\mathcal M};S^1)$. We say that bounded map $T\colon L^p({\mathcal M})\to N})$ is $S^1$-bounded (resp. $S^1$-contractive) if $T\otimes I_{S^1}$ extends to contractive) $T\overline{\otimes} from $ M};S^1)$ into N};S^1)$. show completely positive $S^1$-bo...

Let L = −∆+ V be a Schrödinger operator on R, d ≥ 3, where V is a nonnegative function, V 6= 0, and belongs to the reverse Hölder class RHd/2. The purpose of this paper is three-fold. First, we prove a version of the classical theorem of Jones and Journé on weak∗-convergence in H L(R ). Secondly, we give a bilinear decomposition for the product space H L(R )×BMOL(R). Finally, we study the commu...

The Stokes semigroup on a bounded domain is an analytic semigroup on spaces of bounded functions as was recently shown by the authors based on an a priori L∞-estimate for solutions to the linear Stokes equations. In this paper, we extend our approach to exterior domains and prove that the Stokes semigroup is uniquely extendable to an analytic semigroup on spaces of bounded functions.