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- W2011031715 abstract "If $H geqslant 0$ is the generator of a hypercontractive semigroup (HCSG), it is known that ${(H + 1)^{ - 1/2}}$ is a bounded operator from ${L^p}$ to ${L^p},1 leqslant p leqslant infty$. We prove that ${(H + 1)^{ - 1/2}}$ is bounded from ${L^2}$ to the Orlicz space ${L^2}{text { I}}{{text {n}}^ + }L$, basing the proof on the uniform semiboundedness of the operator $H + V$, for suitable $V$. We also prove by an interpolation argument, that ${(H + 1)^{ - 1/2}}$ is bounded from ${L^p}$ to ${L^p}{text { I}}{{text {n}}^ + }L,2 leqslant p < infty$. Another interpolation argument shows that ${(H + 1)^{ - 1/2}}$ is bounded from ${L^p}{({text {I}}{{text {n}}^ + }L)^m}$ to ${L^p}{({text {I}}{{text {n}}^ + }L)^{m + 1}}$ and $m$ a positive integer. Finally, we identify the topological duals of the spaces mentioned above." @default.
- W2011031715 created "2016-06-24" @default.
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- W2011031715 date "1975-01-01" @default.
- W2011031715 modified "2023-09-23" @default.
- W2011031715 title "Hypercontractive semigroups and Sobolev’s inequality" @default.
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- W2011031715 doi "https://doi.org/10.1090/s0002-9947-1975-0511867-0" @default.
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