Monotonicity Property of Logarithmic Sobolev Inequalities

摘要

An Argument allowing the extension of index P logarithmic Sobolev inequalities to211u001eindex q is presented and is shown to depend on monotonicity of (1-1/p)c(p), where 211u001ec(p) is the principal coefficient function. This generalizes an original result 211u001eof Stroock to the effect that index 2 may be extended to index p.