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Sobolev inequalities for weight spaces and supercontractivity. (English) Zbl 0344.46072


MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
35B45 A priori estimates in context of PDEs
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References:

[1] Leonard Gross, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1975), no. 4, 1061 – 1083. · Zbl 0318.46049
[2] G. Feissner, A Gaussian measure analogue to Sobolev’s inequality, Thesis, Cornell University, Ithaca, N. Y., 1972.
[3] Barry Simon and Raphael Høegh-Krohn, Hypercontractive semigroups and two dimensional self-coupled Bose fields, J. Functional Analysis 9 (1972), 121 – 180. · Zbl 0241.47029
[4] Edward Nelson, The free Markoff field, J. Functional Analysis 12 (1973), 211 – 227. · Zbl 0273.60079
[5] J.-P. Eckmann, Hypercontractivity for anharmonic oscillators, J. Functional Analysis 16 (1974), 388 – 404. With an appendix by D. Pearson. · Zbl 0285.47032
[6] M. A. Krasnosel\(^{\prime}\)skiĭ and Ja. B. Rutickiĭ, Convex functions and Orlicz spaces, Translated from the first Russian edition by Leo F. Boron, P. Noordhoff Ltd., Groningen, 1961.
[7] J. Rosen, Logarithmic Sobolev inequalities and supercontractivity for anharmonic oscillators, Thesis, Princeton University, 1974.
[8] Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. · Zbl 0148.12601
[9] Jay Rosen and Barry Simon, Fluctuations in \?(\?) processes, Ann. Probability 4 (1976), no. 2, 155 – 174. · Zbl 0337.60064
[10] C. Loewner, Über konvexe Matrixfunctionen, Math. Z. 38 (1934), 177-216.
[11] Po-fang Hsieh and Yasutaka Sibuya, On the asymptotic integration of second order linear ordinary differential equations with polynomial coefficients, J. Math. Anal. Appl. 16 (1966), 84 – 103. · Zbl 0161.05803
[12] Barry Simon, Coupling constant analyticity for the anharmonic oscillator. (With appendix), Ann. Physics 58 (1970), 76 – 136.
[13] Barry Simon, Pointwise bounds on eigenfunctions and wave packets in \?-body quantum systems. III, Trans. Amer. Math. Soc. 208 (1975), 317 – 329. · Zbl 0305.35078
[14] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa (3) 13 (1959), 115 – 162. · Zbl 0088.07601
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