Nash type inequalities for fractional powers of non-negative self-adjoint operators

被引：34

作者：

Bendikov, Alexander

Maheux, Patrick

机构：

[1] Univ Wroclaw, Inst Math, PL-50384 Wroclaw, Poland

[2] Univ Orleans, Dept Math, MAPMO Federat Denis Poisson, F-45067 Orleans 2, France

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2007年 / 359卷 / 07期

关键词：

Nash inequality; fractional powers of operators; semigroup of operators; logarithmic Sobolev inequality; ultracontractivity property; Dirichlet form;

D O I：

10.1090/S0002-9947-07-04020-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Assuming that a Nash type inequality is satisfied by a non-negative self-adjoint operator A, we prove a Nash type inequality for the fractional powers A(alpha) of A. Under some assumptions, we give ultracontractivity bounds for the semigroup (T-t,T-alpha) generated by -A(alpha).

引用

页码：3085 / 3097

页数：13

共 50 条

[1] NON-NEGATIVE PERTURBATIONS OF NON-NEGATIVE SELF-ADJOINT OPERATORS
Adamyan, Vadym
METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY, 2007, 13 (02): : 103 - 109
[2] Hardy spaces associated with non-negative self-adjoint operators
Dekel, Shai
Kerkyacharian, Gerard
Kyriazis, George
Petrushev, Pencho
STUDIA MATHEMATICA, 2017, 239 (01) : 17 - 54
[3] Pseudodifferential Operators on Spaces of Distributions Associated with Non-negative Self-Adjoint Operators
Georgiadis, A. G.
Nielsen, M.
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2017, 23 (02) : 344 - 378
[4] Pseudodifferential Operators on Spaces of Distributions Associated with Non-negative Self-Adjoint Operators
A. G. Georgiadis
M. Nielsen
Journal of Fourier Analysis and Applications, 2017, 23 : 344 - 378
[5] Spectral stability of general non-negative self-adjoint operators with applications to Neumann-type operators
Burenkov, Victor I.
Lamberti, Pier Domenico
JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 233 (02) : 345 - 379
[6] Rational approximations to fractional powers of self-adjoint positive operators
Lidia Aceto
Paolo Novati
Numerische Mathematik, 2019, 143 : 1 - 16
[7] Rational approximations to fractional powers of self-adjoint positive operators
Aceto, Lidia
Novati, Paolo
NUMERISCHE MATHEMATIK, 2019, 143 (01) : 1 - 16
[8] Spectral multipliers on spaces of distributions associated with non-negative self-adjoint operators
Georgiadis, Athanasios G.
Nielsen, Morten
JOURNAL OF APPROXIMATION THEORY, 2018, 234 : 1 - 19
[9] POWERS AND COMMUTATIVITY OF SELF-ADJOINT OPERATORS
UCHIYAMA, M
MATHEMATISCHE ANNALEN, 1994, 300 (04) : 643 - 647
[10] On the reduction of powers of self-adjoint operators
Kebli, Salima
Mortad, Mohammed Hichem
QUAESTIONES MATHEMATICAE, 2025,

← 1 2 3 4 5 →