L∞-estimates for the torsion function and L∞-growth of semigroups satisfying Gaussian bounds
نویسنده
چکیده
We investigate selfadjoint C0-semigroups on Euclidean domains satisfying Gaussian upper bounds. Major examples are semigroups generated by second order uniformly elliptic operators with Kato potentials and magnetic fields. We study the long time behaviour of the L∞ operator norm of the semigroup. As an application we prove a new L∞-bound for the torsion function of a Euclidean domain that is close to optimal. MSC 2010: 35P99, 35K08, 35J25
منابع مشابه
Hardy Spaces for Semigroups with Gaussian Bounds
Let Tt = e−tL be a semigroup of self-adjoint linear operators acting on L(X,μ), where (X, d, μ) is a space of homogeneous type. We assume that Tt has an integral kernel Tt(x, y) which satisfies the upper and lower Gaussian bounds: C1 μ(B(x, √ t)) exp ( −c1d(x, y)/t ) ≤ Tt(x, y) ≤ C2 μ(B(x, √ t)) exp ( −c2d(x, y)/t ) . By definition, f belongs to H L if ‖f‖H1 L = ‖ supt>0 |Ttf(x)|‖L1(X,μ) < ∞. W...
متن کاملTHE DUALITY OF THE L?-REPRESENTATION ALGEBRA ?(S ) OF A FOUNDATION SEMIGROUP S AND FUNCTION ALGEBRAS
In the present paper for a large family of topological semigroups, namely foundation semigroups, for which topological groups and discrete semigroups are elementary examples, it is shown that ?(S) is the dual of a function algebra.
متن کاملPERMUTATION GROUPS WITH BOUNDED MOVEMENT ATTAINING THE BOUNDS FOR ODD PRIMES
Let G be a transitive permutation group on a set ? and let m be a positive integer. If no element of G moves any subset of ? by more than m points, then |? | [2mp I (p-1)] wherep is the least odd primedividing |G |. When the bound is attained, we show that | ? | = 2 p q ….. q where ? is a non-negative integer with 2 < p, r 1 and q is a prime satisfying p < q < 2p, ? = 0 or 1, I i n....
متن کاملSome inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm
Let A = (an;k)n;k1 and B = (bn;k)n;k1 be two non-negative ma-trices. Denote by Lv;p;q;B(A), the supremum of those L, satisfying the followinginequality:k Ax kv;B(q) L k x kv;B(p);where x 0 and x 2 lp(v;B) and also v = (vn)1n=1 is an increasing, non-negativesequence of real numbers. In this paper, we obtain a Hardy-type formula forLv;p;q;B(H), where H is the Hausdor matrix and 0 < q p 1. Also...
متن کاملBounds on the restrained Roman domination number of a graph
A {em Roman dominating function} on a graph $G$ is a function$f:V(G)rightarrow {0,1,2}$ satisfying the condition that everyvertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex$v$ for which $f(v) =2$. {color{blue}A {em restrained Roman dominating}function} $f$ is a {color{blue} Roman dominating function if the vertices with label 0 inducea subgraph with no isolated vertex.} The wei...
متن کامل