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Hypercontractivity for the heat semigroup for ultraspherical polynomials and on the n-sphere. (English) Zbl 0506.46022


MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47A30 Norms (inequalities, more than one norm, etc.) of linear operators
47D03 Groups and semigroups of linear operators
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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