04936nam 22007813 450 991095375680332120231110232605.097814704662821470466287(CKB)4940000000609979(MiAaPQ)EBC6715028(Au-PeEL)EBL6715028(RPAM)22495358(PPN)25825713X(OCoLC)1264677087(EXLCZ)99494000000060997920210901d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierHardy-Littlewood and Ulyanov Inequalities1st ed.Providence :American Mathematical Society,2021.©2021.1 online resource (132 pages)Memoirs of the American Mathematical Society ;v.271"May 2021, volume 271, number 1325 (second of 7 numbers)."9781470447588 1470447584 Includes bibliographical references.Auxiliary results -- Polynomial inequalities of Nikolʹskii-Stechkin-Boas-types -- Basic properties of fractional moduli of smoothness -- Hardy-Littlewood-Nikolʹskii 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."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"--Provided by publisher.Memoirs of the American Mathematical Society Inequalities (Mathematics)Hardy-Littlewood methodSmoothness of functionsApproximations and expansions -- Approximations and expansions -- Multidimensional problemsmscHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- MultipliersmscReal functions -- Inequalities -- Inequalities involving derivatives and differential and integral operatorsmscFunctional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of "smooth'' functions, embedding theorems, trace theoremsmscReal functions -- Functions of one variable -- Fractional derivatives and integralsmscApproximations and expansions -- Approximations and expansions -- Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities)mscReal functions -- Polynomials, rational functions -- Polynomials: analytic properties, etc.mscApproximations and expansions -- Approximations and expansions -- Approximation by polynomialsmscInequalities (Mathematics)Hardy-Littlewood method.Smoothness of functions.Approximations and expansions -- Approximations and expansions -- Multidimensional problems.Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Multipliers.Real functions -- Inequalities -- Inequalities involving derivatives and differential and integral operators.Functional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of "smooth'' functions, embedding theorems, trace theorems.Real functions -- Functions of one variable -- Fractional derivatives and integrals.Approximations and expansions -- Approximations and expansions -- Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities).Real functions -- Polynomials, rational functions -- Polynomials: analytic properties, etc..Approximations and expansions -- Approximations and expansions -- Approximation by polynomials.515/.2641A6342B1526D1046E3526A3341A1726C0541A10mscKolomoitsev Yurii1801806Tikhonov Sergey1801807MiAaPQMiAaPQMiAaPQBOOK9910953756803321Hardy-Littlewood and Ulyanov Inequalities4347203UNINA