LEADER 03611nam 2200613 a 450 001 9910438146503321 005 20200520144314.0 010 $a1-299-33565-9 010 $a3-0348-0548-9 024 7 $a10.1007/978-3-0348-0548-3 035 $a(CKB)2670000000337134 035 $a(EBL)1082179 035 $a(OCoLC)828303009 035 $a(SSID)ssj0000879895 035 $a(PQKBManifestationID)11956608 035 $a(PQKBTitleCode)TC0000879895 035 $a(PQKBWorkID)10873224 035 $a(PQKB)11298607 035 $a(DE-He213)978-3-0348-0548-3 035 $a(MiAaPQ)EBC1082179 035 $a(PPN)168307456 035 $a(EXLCZ)992670000000337134 100 $a20130107d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aVariable Lebesgue spaces $efoundations and harmonic analysis /$fDavid V. Cruz-Uribe, Alberto Fiorenza 205 $a1st ed. 2013. 210 $aHeidelberg ;$aNew York $cBirkhauser$dc2013 215 $a1 online resource (315 p.) 225 0$aApplied and numerical harmonic analysis 300 $aDescription based upon print version of record. 311 $a3-0348-0757-0 311 $a3-0348-0547-0 320 $aIncludes bibliographical references and indexes. 327 $a 1 Introduction -- 2 Structure of Variable Lebesgue Spaces -- 3 The Hardy-Littlewood Maximal Operator.- 4 Beyond Log-Hölder Continuity -- 5 Extrapolation in the Variable Lebesgue Spaces -- 6 Basic Properties of Variable Sobolev Spaces -- Appendix: Open Problems -- Bibliography -- Symbol Index -- Author Index -- Subject Index.        . 330 $aThis book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, and for their applications to problems in physics and image processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-on approach that makes clear the similarities and differences between the variable and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewood maximal operator is completely developed, and the connections between variable Lebesgue spaces and the weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Riesz potentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolation from the theory of weighted norm inequalities. The final chapter applies the results from previous chapters to prove basic results about variable Sobolev spaces. 410 0$aApplied and Numerical Harmonic Analysis,$x2296-5009 606 $aLebesgue integral 606 $aHarmonic analysis 615 0$aLebesgue integral. 615 0$aHarmonic analysis. 676 $a515.43 700 $aCruz-Uribe$b David V$066274 701 $aFiorenza$b Alberto$0521175 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438146503321 996 $aVariable lebesgue spaces$9832700 997 $aUNINA