LEADER 04936nam 22007813 450 001 9910953756803321 005 20231110232605.0 010 $a9781470466282 010 $a1470466287 035 $a(CKB)4940000000609979 035 $a(MiAaPQ)EBC6715028 035 $a(Au-PeEL)EBL6715028 035 $a(RPAM)22495358 035 $a(PPN)25825713X 035 $a(OCoLC)1264677087 035 $a(EXLCZ)994940000000609979 100 $a20210901d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHardy-Littlewood and Ulyanov Inequalities 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2021. 210 4$dİ2021. 215 $a1 online resource (132 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.271 300 $a"May 2021, volume 271, number 1325 (second of 7 numbers)." 311 08$a9781470447588 311 08$a1470447584 320 $aIncludes bibliographical references. 327 $aAuxiliary results -- Polynomial inequalities of Nikol?skii-Stechkin-Boas-types -- Basic properties of fractional moduli of smoothness -- Hardy-Littlewood-Nikol?skii inequalities for trigonometric polynomials -- General form of the Ulyanov inequality for moduli of smoothness, K-functionals, and their realizations -- Sharp Ulyanov inequalities for K-functionals and realizations -- Sharp Ulyanov inequalities for moduli of smoothness -- Sharp Ulyanov inequalities for realizations of K-functionals related to Riesz derivatives and corresponding moduli of smoothness -- Sharp Ulyanov inequality via Marchaud inequality -- Sharp Ulyanov and Kolyada inequalities in Hardy spaces -- (Lp, Lq) inequalities of Ulyanov-type involving derivatives -- Embedding theorems for function spaces. 330 $a"We give the full solution of the following problem: obtain sharp inequalities between the moduli of smoothness f, t)q and (f, t)p for 0 < p < q . A similar problem for the generalized K-functionals and their realizations between the couples (Lp,W p ) and (Lq,W q ) is also solved"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aInequalities (Mathematics) 606 $aHardy-Littlewood method 606 $aSmoothness of functions 606 $aApproximations and expansions -- Approximations and expansions -- Multidimensional problems$2msc 606 $aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Multipliers$2msc 606 $aReal functions -- Inequalities -- Inequalities involving derivatives and differential and integral operators$2msc 606 $aFunctional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of "smooth'' functions, embedding theorems, trace theorems$2msc 606 $aReal functions -- Functions of one variable -- Fractional derivatives and integrals$2msc 606 $aApproximations and expansions -- Approximations and expansions -- Inequalities in approximation (Bernstein, Jackson, Nikol'skii?-type inequalities)$2msc 606 $aReal functions -- Polynomials, rational functions -- Polynomials: analytic properties, etc.$2msc 606 $aApproximations and expansions -- Approximations and expansions -- Approximation by polynomials$2msc 615 0$aInequalities (Mathematics) 615 0$aHardy-Littlewood method. 615 0$aSmoothness of functions. 615 7$aApproximations and expansions -- Approximations and expansions -- Multidimensional problems. 615 7$aHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Multipliers. 615 7$aReal functions -- Inequalities -- Inequalities involving derivatives and differential and integral operators. 615 7$aFunctional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of "smooth'' functions, embedding theorems, trace theorems. 615 7$aReal functions -- Functions of one variable -- Fractional derivatives and integrals. 615 7$aApproximations and expansions -- Approximations and expansions -- Inequalities in approximation (Bernstein, Jackson, Nikol'skii?-type inequalities). 615 7$aReal functions -- Polynomials, rational functions -- Polynomials: analytic properties, etc.. 615 7$aApproximations and expansions -- Approximations and expansions -- Approximation by polynomials. 676 $a515/.26 686 $a41A63$a42B15$a26D10$a46E35$a26A33$a41A17$a26C05$a41A10$2msc 700 $aKolomoitsev$b Yurii$01801806 701 $aTikhonov$b Sergey$01801807 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910953756803321 996 $aHardy-Littlewood and Ulyanov Inequalities$94347203 997 $aUNINA