Titlebook: Harmonic Function Theory; Sheldon Axler,Paul Bourdon,Wade Ramey Textbook 2001Latest edition Springer Science+Business Media New York 2001

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Sheldon Axler,Paul Bourdon,Wade RameyWe introduce a class of aggregation functions by the help of continuous .-norms and .-conorms. The general functional forms of such aggregations is determined. Associativity and idempotency are also studied separately.

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Harmonic Hardy Spaces,In Chapter 1 we defined the Poisson integral of a function . ∈ C(S) to be the function . on . given by.We now extend this definition: for μ a complex Borel measure on ., the Poisson integral of μ, denoted μ[p], is the function on . defined by.Differentiating under the integral sign in 6.2, we see that P [μ] is har-monic on .

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Harmonic Bergman Spaces,Throughout this chapter, p denotes a number satisfying 1 ≤ . < ∞. The ... (Ω) is the set of harmonic functions . on Ω such that

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Annular Regions,An . is a set of the form {. ∈ .. : .. < |.| < ..}; here .. ∈ [0, ∞) and .. ∈ (0, ∞]. Thus an annular region is the region between two concentric spheres, or is a punctured ball, or is the complement of a closed ball, or is .. {0}.

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