Varopoulos, N. Th. Hardy-Littlewood theory for semigroups. (English) Zbl 0608.47047 J. Funct. Anal. 63, 240-260 (1985). Some well-known inequalities for the diffusion heat equation are generalized on the case of symmetric submarkovian semigroups. Some applications for other semigroups are presented. Reviewer: A.L.Davidowicz Cited in 5 ReviewsCited in 132 Documents MSC: 47D07 Markov semigroups and applications to diffusion processes 47D03 Groups and semigroups of linear operators 47B38 Linear operators on function spaces (general) 47A30 Norms (inequalities, more than one norm, etc.) of linear operators Keywords:Hardy-Littlewood theory; inequalities; diffusion heat equation; symmetric submarkovian semigroups PDFBibTeX XMLCite \textit{N. Th. Varopoulos}, J. Funct. Anal. 63, 240--260 (1985; Zbl 0608.47047) Full Text: DOI References: [1] Deny, J., Potential Theory (July 2-10, 1969), C.I.M.E., Ier cycle: C.I.M.E., Ier cycle Stresa [2] Fukushima, M., Dirichlet Forms and Markov Processes (1980), North-Holland/Kodansha: North-Holland/Kodansha Amsterdam · Zbl 0422.31007 [3] Stein, E. M., Topics in Harmonic Analysis Related to Littlewood-Paley Theory (1970), Princeton Univ. Press: Princeton Univ. Press Princeton, N.J · Zbl 0193.10502 [4] Varopoulus, N. Th, C. R. Acad. Sci. Ser. I Math., 298, 465-468 (1984) [5] Varopoulos, N. Th, Isoperimetric inequalities and Markov chains, J. Func. Analysis, 63, 215-239 (1985) · Zbl 0573.60059 [6] Varopoulos, N. Th, C. R. Acad. Sci. Ser. I Math., 298, 233-236 (1984) [7] Varopoulos, N. Th, C. R. Acad. Sci. Ser. I Math., 299, 651-654 (1984) [8] Yosida, K., Functional Analysis (1978), Springer-Verlag: Springer-Verlag Berlin/New York · Zbl 0152.32102 [9] Duren, P. L., Theory of \(H^p\) spaces (1970), Academic Press: Academic Press New York · Zbl 0215.20203 [10] Stein, E. M., Singular Integrals and Differentiability Properties of Functions (1971), Princeton Univ. Press: Princeton Univ. Press Princeton, N.J [11] Herz, C. S., J. Math. Mech., 18, No. (4), 283-324 (1968) [13] Moser, J., Comm. Pure Appl. Math., XVII (1964) [14] Moser, J., Comm. Pure Appl. Math., XXIV (1971) [15] Hardy, G. H.; Littlewood, J. E., J. Reine Angew. Math., 167, 405-423 (1932) [16] Duren, P. L.; Romberg, B. W.; Shields, A. L., Reine Angew. Math., 238, 32-60 (1969) [17] Folland, G. B.; Stein, E. M., Hardy Spaces on Homogeneous Groups, (Mathematical Notes (1982), Princeton Univ. Press: Princeton Univ. Press Princeton, N.J) · Zbl 0508.42025 [19] Bishop, R. L.; Crittenden, R. J., Geometry on Manifolds (1964), Academic Press: Academic Press New York · Zbl 0132.16003 [20] Varopoulos, N. Th, J. Funct. Anal., 44, 359-380 (1981) [21] Osserman, R., Bull. Amer. Math. Soc., 84, No. 6, 1192-1197 (1978) [22] Yau, S.-T, Ann. Sci. Ecole Norm. Sup., 8, 487-507 (1975), (4) [23] Lohoue, N., C. R. Acad. Sci. Ser A, 290, 605-608 (1980) [24] Varopoulos, N. Th, A potential theoretic property of soluble groups, Bull. Sci. Math., 108, No. 3, 263-273 (1984) · Zbl 0546.60008 [25] Zygmund, A., (Trigonometric Series, Vol. I and II (1959), Cambridge Univ. Press: Cambridge Univ. Press London) · JFM 58.0280.01 [26] Neveu, J., Martingales a temps discret (1972), Masson & Cie: Masson & Cie Paris [27] Cheeger, J.; Gromov, M.; Taylor, M., J. Differential Geometry, 17, 17-53 (1982) [28] Varopoulos, N. Th, C. R. Acad. Sci. Ser. I Math. (1985) [30] Davies, E. B.; Simon, B., J. Funct. Anal., 59, No. 2, 335-395 (1985) [31] Varopoulos, N. Th, C. R. Acad. Sci. Ser. I Math., 300, 62-617 (1985) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.