Logarithmic Sobolev inequalities and the growth of ๐ฟ^{๐} norms
Logarithmic Sobolev inequalities and the growth of ๐ฟ^{๐} norms
We show that many of the recent results on exponential integrability of Lip 1 functions, when a logarithmic Sobolev inequality holds, follow from more fundamental estimates of the growth of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Superscript p"> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>p</mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding="application/x-tex">L^{p}</mml:annotation> </mml:semantics> </mml:math> โฆ