Hardy Spaces on Homogeneous Groups (eBook)

Gerald B. Folland, Elias M. Stein (Autoren)

eBook Download: PDF

2020
Princeton University Press (Verlag)
978-0-691-22245-5 (ISBN)

Infos

The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in Rn of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development, a systematic exposition of some of the main parts of the theory is now desirable. In addition to this exposition, these notes contain a recasting of the theory in the more general setting where the underlying Rn is replaced by a homogeneous group.The justification for this wider scope comes from two sources: 1) the theory of semi-simple Lie groups and symmetric spaces, where such homogeneous groups arise naturally as "e;boundaries,"e; and 2) certain classes of non-elliptic differential equations (in particular those connected with several complex variables), where the model cases occur on homogeneous groups. The example which has been most widely studied in recent years is that of the Heisenberg group.

Produkt-Details

• Erscheint lt. Verlag: 8.12.2020
• Reihe/Serie: Mathematical Notes
• Reihe/Serie: Mathematical Notes
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Schlagworte: absolute value • Addition • Adjoint • "admissible • Antiderivative • Antiisomorphism • approximate identity • Approximation • area integral • associated (to a ball) • Atom • atomic decomposition • atomic Hardy space • automorphism • Ball • Banach space • Boundary value problem • bounded function • bounded mean oscillation • boundedness • Brownian motion • Campanato space • Campbell-Hausdorff formul • Cauchy–Riemann equations • Central series • Characteristic function (probability theory) • Characterization (mathematics) • Chebyshev's inequality • Class function (algebra) • coefficient • combination • commutative approximate identity • Complex Analysis • Complex conjugate • complex number • conjecture • Constant function • Constants • Constant term • continuous function • convolution • corollary • Derivatives and multiindices • differential equation • Differential operator • Dilations • Dimension (vector space) • Distribution Function • dual space • Eigenvalues and Eigenvectors • equivalence class • estimation • Euclidean Vector • existential quantification • Exponential map (Lie theory) • Fatou's theorem • Fourier transform • Function (mathematics) • function space • graded • Grand maximal function • Green's Theorem • Hardy-Littlewood maximal function • Hardy space • Harmonic Analysis • Harmonic function • heat equation • Heat kernel • heat semigroup • Heisenberg group • hilbert space • holomorphic function • Integer • interpolation theorem • isotropic degree • Iwasawa decomposition • kernel of type • Laplace's equation • Lie algebra • Lie group • Linear combination • Linear space (geometry) • Linear span • Littlewood-Paley function • lower central series • Lp space • Lusin function • Majorization • Maximal compact subgroup • maximal function • Maximal functions • Maximum principle • mean value theorem • Natural number • Nilpotent • non-abelian • nonincreasing rearrangement • nontangential maximal function • Norms • One-parameter group • Orthonormal basis • Other operations on functions" • p-admissible • Pairing • partial differential equation • partition of unity • Poisson kernel • Poisson-Szegö kernel • polynomial • polyradial • positive operator • quasinorms • scalar multiplication • scientific notation • Semigroup • seminorms • Singular integral • Smoothness • Special case • Square (algebra) • SUBGROUP • Subset • Support (mathematics) • symmetric space • Tangent vector • Temperature • Theorem • Topological space • Topology • Upper half-plane • Variable (mathematics) • Vector field
• ISBN-10: 0-691-22245-2 / 0691222452
• ISBN-13: 978-0-691-22245-5 / 9780691222455