03493nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001800172072001700190072002300207072001600230100008600246245008300332250001800415264007500433300004400508336002600552337002600578338003600604347002400640490005300664505069700717520117601414650002202590650003002612650002202642650003902664710003402703773002602737776003602763776003602799776003602835830006002871856004602931912001402977912001502991999001703006978-3-031-56500-7DE-He21320251030112640.0cr nn 008mamaa240721s2024    sz |    s    |||| 0|eng d  a97830315650079978-3-031-56500-77 a10.1007/978-3-031-56500-72doi 4aQA403.5-404.5 7aPBKF2bicssc 7aMAT0340002bisacsh 7aPBKF2thema1 aGrafakos, Loukas.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98097110aFundamentals of Fourier Analysish[electronic resource] /cby Loukas Grafakos.  a1st ed. 2024. 1aCham :bSpringer International Publishing :bImprint: Springer,c2024.  aXVI, 407 p. 29 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aGraduate Texts in Mathematics,x2197-5612 ;v3020 a1 Introductory Material -- 2 Fourier Transforms, Tempered Distributions, Approximate Identities -- 3 Singular Integrals -- 4 Vector-Valued Singular Integrals and Littlewood–Paley Theory -- 5 Fractional Integrability or Differentiability and Multiplier Theorems -- 6 Bounded Mean Oscillation -- 7 Hardy Spaces -- 8 Weighted Inequalities -- Historical Notes -- Appendix A Orthogonal Matrices -- Appendix B Subharmonic Functions -- Appendix C Poisson Kernel on the Unit Strip -- Appendix D Density for Subadditive Operators -- Appendix E Transposes and Adjoints of Linear Operators -- Appendix F Faa di Bruno Formula -- Appendix G Besicovitch Covering Lemma -- Glossary -- References -- Index.  aThis self-contained text introduces Euclidean Fourier Analysis to graduate students who have completed courses in Real Analysis and Complex Variables. It provides sufficient content for a two course sequence in Fourier Analysis or Harmonic Analysis at the graduate level. In true pedagogical spirit, each chapter presents a valuable selection of exercises with targeted hints that will assist the reader in the development of research skills. Proofs are presented with care and attention to detail. Examples are provided to enrich understanding and improve overall comprehension of the material. Carefully drawn illustrations build intuition in the proofs. Appendices contain background material for those that need to review key concepts. Compared with the author’s other GTM volumes (Classical Fourier Analysis and Modern Fourier Analysis), this text offers a more classroom-friendly approach as it contains shorter sections, more refined proofs, and a wider range of exercises. Topics include the Fourier Transform, Multipliers, Singular Integrals, Littlewood–Paley Theory, BMO, Hardy Spaces, and Weighted Estimates, and can be easily covered within two semesters. 0aFourier analysis. 0aHarmonic analysis.97230114aFourier Analysis.24aAbstract Harmonic Analysis.9723052 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303156499408iPrinted edition:z978303156501408iPrinted edition:z9783031565021 0aGraduate Texts in Mathematics,x2197-5612 ;v30297230840uhttps://doi.org/10.1007/978-3-031-56500-7  aZDB-2-SMA  aZDB-2-SXMS  c61779d61779