LEADER 04197nam 2200757 450 001 9910787601603321 005 20211209000625.0 010 $a3-11-028190-2 024 7 $a10.1515/9783110281903 035 $a(CKB)2670000000523356 035 $a(EBL)1130360 035 $a(SSID)ssj0001121899 035 $a(PQKBManifestationID)11634434 035 $a(PQKBTitleCode)TC0001121899 035 $a(PQKBWorkID)11058254 035 $a(PQKB)11421608 035 $a(MiAaPQ)EBC1130360 035 $a(DE-B1597)175787 035 $a(OCoLC)1002221767 035 $a(OCoLC)1004868836 035 $a(OCoLC)1011447696 035 $a(OCoLC)870589848 035 $a(OCoLC)979955084 035 $a(OCoLC)987934168 035 $a(OCoLC)992524325 035 $a(OCoLC)999354714 035 $a(DE-B1597)9783110281903 035 $a(Au-PeEL)EBL1130360 035 $a(CaPaEBR)ebr10838307 035 $a(CaONFJC)MIL574214 035 $a(PPN)182938786 035 $a(EXLCZ)992670000000523356 100 $a20140221h20142014 uy| 0 101 0 $aeng 135 $aurnn#---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aFunction classes on the unit disc $ean introduction /$fMiroslav Pavlovic? 210 1$aBerlin :$cDe Gruyter,$d[2014] 210 4$d©2014 215 $a1 online resource (463 p.) 225 0 $aDe Gruyter Studies in Mathematics ;$v52 300 $aDescription based upon print version of record. 311 0 $a3-11-028123-6 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tPreface /$rPavlovi?, Miroslav --$tContents --$t1. The Poisson integral and Hardy spaces --$t2. Subharmonic functions and Hardy spaces --$t3. Subharmonic behavior and mixed norm spaces --$t4. Taylor coefficients with applications --$t5. Besov spaces --$t6. The dual of H1 and some related spaces --$t7. Littlewood-Paley theory --$t8. Lipschitz spaces of first order --$t9. Lipschitz spaces of higher order --$t10. One-to-one mappings --$t11. Coefficients multipliers --$t12. Toward a theory of vector-valued spaces --$tA. Quasi-Banach spaces --$tB. Interpolation and maximal functions --$tBibliography --$tIndex 330 $aThis monograph contains a study on various function classes, a number of new results and new or easy proofs of old results (Fefferman-Stein theorem on subharmonic behavior, theorems on conjugate functions and fractional integration on Bergman spaces, Fefferman's duality theorem), which are interesting for specialists; applications of the Hardy-Littlewood inequalities on Taylor coefficients to (C, ?)-maximal theorems and (C, ?)-convergence; a study of BMOA, due to Knese, based only on Green's formula; the problem of membership of singular inner functions in Besov and Hardy-Sobolev spaces; a full discussion of g-function (all p ? 0) and Calderón's area theorem; a new proof, due to Astala and Koskela, of the Littlewood-Paley inequality for univalent functions; and new results and proofs on Lipschitz spaces, coefficient multipliers and duality, including compact multipliers and multipliers on spaces with non-normal weights. It also contains a discussion of analytic functions and lacunary series with values in quasi-Banach spaces with applications to function spaces and composition operators. Sixteen open questions are posed. The reader is assumed to have a good foundation in Lebesgue integration, complex analysis, functional analysis, and Fourier series. Further information can be found at the author's website at http://poincare.matf.bg.ac.rs/~pavlovic. 410 3$aDe Gruyter Studies in Mathematics 606 $aFunctional analysis 610 $aBergman Space. 610 $aBesov-Lipschitz Space. 610 $aBounded Mean Oscillation. 610 $aHardy Space. 610 $aLittlewood-Paley g-Function. 615 0$aFunctional analysis. 676 $a510 686 $aSK 600$qSEPA$2rvk 700 $aPavlovic?$b Miroslav$0505575 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910787601603321 996 $aFunction classes on the unit disc$91469084 997 $aUNINA