Harnack Inequalities for Log-Sobolev Functions and Estimates of Log-Sobolev Constants
نویسندگان
چکیده
منابع مشابه
Strong Logarithmic Sobolev Inequalities for Log-Subharmonic Functions
We prove an intrinsic equivalence between strong hypercontractivity (sHC) and a strong logarithmic Sobolev inequality (sLSI) for the cone of logarithmically subharmonic (LSH) functions. We introduce a new large class of measures, Euclidean regular and exponential type, in addition to all compactly-supported measures, for which this equivalence holds. We prove a Sobolev density theorem through L...
متن کاملSharp Stability Theorems for the Anisotropic Sobolev and Log-sobolev Inequalities on Functions of Bounded Variation
Combining rearrangement techniques with Gromov’s proof (via optimal mass transportation) of the 1-Sobolev inequality, we prove a sharp quantitative version of the anisotropic Sobolev inequality on BV (R). As a corollary of this result, we also deduce a sharp stability estimate for the anisotropic 1-log-Sobolev inequality.
متن کاملModified Log-sobolev Inequalities and Isoperimetry
We find sufficient conditions for a probability measure μ to satisfy an inequality of the type ∫ Rd fF ( f ∫ Rd f 2 dμ ) dμ ≤ C ∫ Rd f2c∗ ( |∇f | |f | ) dμ + B ∫ Rd f dμ, where F is concave and c (a cost function) is convex. We show that under broad assumptions on c and F the above inequality holds if for some δ > 0 and ε > 0 one has ∫ ε 0 Φ ( δc [ tF ( 1t ) Iμ(t) ]) dt <∞, where Iμ is the isop...
متن کاملLog-sobolev Inequalities with Potential Functions on Pinned Path Groups
We establish a refined version of Gross’s log-Sobolev inequalities on pinned path groups. We explain the reason why it is useful in a lower bound estimate of Schrödinger operators on path spaces.
متن کاملOn Equivalence of Super Log Sobolev and Nash Type Inequalities
We prove the equivalence of Nash type and super log Sobolev inequalities for Dirichlet forms. We also show that both inequalities are equivalent to Orlicz-Sobolev type inequalities. No ultracontractivity of the semigroup is assumed. It is known that there is no equivalence between super log Sobolev or Nash type inequalities and ultracontractivity. We discuss Davies-Simon’s counterexample as bor...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1999
ISSN: 0091-1798
DOI: 10.1214/aop/1022677381