LEADER 03774nam 22006732 450 001 9910457837603321 005 20151005020621.0 010 $a1-107-18249-2 010 $a0-511-64514-7 010 $a9786612389719 010 $a1-282-38971-8 010 $a0-511-64923-1 010 $a0-511-28868-9 010 $a0-511-57390-1 010 $a0-511-75521-X 010 $a0-511-28936-7 035 $a(CKB)1000000000351895 035 $a(EBL)311280 035 $a(OCoLC)476097547 035 $a(SSID)ssj0000361602 035 $a(PQKBManifestationID)12089371 035 $a(PQKBTitleCode)TC0000361602 035 $a(PQKBWorkID)10353076 035 $a(PQKB)11644968 035 $a(UkCbUP)CR9780511755217 035 $a(MiAaPQ)EBC311280 035 $a(PPN)140847499 035 $a(Au-PeEL)EBL311280 035 $a(CaPaEBR)ebr10182299 035 $a(OCoLC)437189162 035 $a(EXLCZ)991000000000351895 100 $a20100422d2007|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aInequalities $ea journey into linear analysis /$fD.J.H. Garling$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2007. 215 $a1 online resource (ix, 335 pages) $cdigital, PDF file(s) 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a0-521-69973-8 311 $a0-521-87624-9 320 $aIncludes bibliographical references (p. 325-329) and indexes. 327 $aHalf-title; Title; Copyright; Contents; Introduction; 1 Measure and integral; 2 The Cauchy--Schwarz inequality; 3 The arithmetic mean-geometric mean inequality; 4 Convexity, and Jensen's inequality; 5 The Lp spaces; 6 Banach function spaces; 7 Rearrangements; 8 Maximal inequalities; 9 Complex interpolation; 10 Real interpolation; 11 The Hilbert transform, and Hilbert's inequalities; 12 Khintchine's inequality; 13 Hypercontractive and logarithmic Sobolev inequalities; 14 Hadamard's inequality; 15 Hilbert space operator inequalities; 16 Summing operators 327 $a17 Approximation numbers and eigenvalues18 Grothendieck's inequality, type and cotype; References; Index of inequalities; Index 330 $aThis book contains a wealth of inequalities used in linear analysis, and explains in detail how they are used. The book begins with Cauchy's inequality and ends with Grothendieck's inequality, in between one finds the Loomis-Whitney inequality, maximal inequalities, inequalities of Hardy and of Hilbert, hypercontractive and logarithmic Sobolev inequalities, Beckner's inequality, and many, many more. The inequalities are used to obtain properties of function spaces, linear operators between them, and of special classes of operators such as absolutely summing operators. This textbook complements and fills out standard treatments, providing many diverse applications: for example, the Lebesgue decomposition theorem and the Lebesgue density theorem, the Hilbert transform and other singular integral operators, the martingale convergence theorem, eigenvalue distributions, Lidskii's trace formula, Mercer's theorem and Littlewood's 4/3 theorem. It will broaden the knowledge of postgraduate and research students, and should also appeal to their teachers, and all who work in linear analysis. 606 $aInequalities (Mathematics) 606 $aFunctional analysis 615 0$aInequalities (Mathematics) 615 0$aFunctional analysis. 676 $a515/.26 700 $aGarling$b D. J. H.$056885 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910457837603321 996 $aInequalities$9258280 997 $aUNINA