By Gerald B. Folland

ISBN-10: 0849384907

ISBN-13: 9780849384905

Summary idea continues to be an crucial beginning for the examine of concrete instances. It exhibits what the final photograph should still seem like and offers effects which are important repeatedly. regardless of this, besides the fact that, there are few, if any introductory texts that current a unified photo of the final summary theory.A direction in summary Harmonic research deals a concise, readable creation to Fourier research on teams and unitary illustration conception. After a quick assessment of the correct components of Banach algebra idea and spectral concept, the e-book proceeds to the elemental proof approximately in the community compact teams, Haar degree, and unitary representations, together with the Gelfand-Raikov lifestyles theorem. the writer devotes chapters to research on Abelian teams and compact teams, then explores brought about representations, that includes the imprimitivity theorem and its purposes. The publication concludes with an off-the-cuff dialogue of a few extra facets of the illustration thought of non-compact, non-Abelian teams.

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**Additional info for A Course in Abstract Harmonic Analysis**

**Example text**

P. Smith, Testing Schatten class Hankel operators and Carleson embeddings via reproducing kernels, J. Lond. Math. Soc. 71 (2005) 172–186. [35] E. Stein, Singular Integrals and Diﬀerentiability Properties of Functions, Princeton University Press, Princeton, New Jersey, 1970. [36] M. Stoll, A characterization of Hardy spaces on the unit ball of Cn , J. Lond. Math. Soc. 48 (1993) 126–136. [37] Z. Wu, A new characterization for Carleson measures and some applications, Integral Equations Operator Theory 71 (2011) 161–180.

Math. Soc. 140 (2012) 4247–4257. [15] P. Duren, Extension of a theorem of Carleson, Bull. Amer. Math. Soc. 75 (1969) 143–146. [16] C. Feﬀerman, E. Stein, H p spaces of several variables, Acta Math. 129 (1972) 137–193. [17] J. Garnett, R. Latter, The atomic decomposition for Hardy spaces in several complex variables, Duke Math. J. 45 (1978) 815–845. [18] M. Gowda, Nonfactorization theorems in weighted Bergman and Hardy spaces on the unit ball of Cn , Trans. Amer. Math. Soc. 277 (1983) 203–212. [19] L.

Bn Putting all together and taking into account that Kzt (1 − |z|2 )−(n+1) , we have that T is in Sp if and only if T p kzt , kzt H2 2 2 2t−1 H 2 (1 − |z| ) is comparable to dλn (z) < ∞. 31]) T p kzt , kzt H2 ≤ T kzt , kzt p H2 = [T t (z)]p , 0

0 and consider the function Ft (z) = T kzt H . If p ≥ 2 and T is in Sp then Ft ∈ Lp (Bn , dλn ).

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