Hardy spaces of analytic multifunctions.
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In this paper we consider a generalization to analytic multifunctions of the classical Hardy space theory of analytic functions on the unit disc. With \K(lambda) = sup (\z\; z is an element of K(lambda)) we define the Nevanlinna class N and the classes HIn this paper, we found a form of interaction which gives the correct binding energy of double 's in . The energy contours and ei and are given.
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We consider A(z)-analytic functions in case when A(z) is antianalytic function. In this paper, the Hardy class for A(z)-analytic functions are introduced and for these classes, the boundary values of the function are investigated. For the Hardy class of functions H1A, an analogue of Fatou's theorem was proved about that the bounded functions have the boundary values. As the main result, the boundary uniqueness theorem for Hardy classes of functions H1A is proven.
Boundary values
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The theory of Hardy spaces dates back to G.H. Hardy and M. Riesz in the early twentieth century. Part of the inspiration here is the celebrated theorem of P. Fatou that a bounded holomorphic function on the unit disk D has radial (indeed nontangential) boundary limits almost everywhere. Hardy and Riesz wished to expand the space of holomorphic functions for which such results could be obtained.
Unit disk
Bounded mean oscillation
Riesz transform
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Hypernucleus
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This paper is concerned with generalizations of the classical Hardy spaces (8, p. 39) and the question of boundary values for functions of these various spaces. The general setting is the “big disk” Δ discussed by Arens and Singer in (1, 2) and by Hoffman in (7). Analytic functions are defined in (1). Classes of such functions corresponding to the Hardy H p spaces are considered and shown to possess boundary values in (2). Contrary to the classical case, such functions do not form a Banach space; hence they are not the functional analytic analogue of the classical spaces. In (3) quasi-analytic functions are defined while in (4) Hardy spaces of such functions are considered and are shown to have boundary values and to form a Banach space.
Boundary values
Function space
Birnbaum–Orlicz space
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Abstract We present some recent results on Hardy spaces of generalized analytic functions on D specifying their link with the analytic Hardy spaces. Their definition can be extended to more general domains Ω . We discuss the way to extend such definitions to more general domains that depends on the regularity of the boundary of the domain ∂Ω. The generalization over general domains leads to the study of the invertibility of composition operators between Hardy spaces of generalized analytic functions; at the end of the paper, we discuss invertibility and Fredholm property of the composition operator C ∅ on Hardy spaces of generalized analytic functions on a simply connected Dini-smooth domain for an analytic symbol ∅.
Composition operator
Operator (biology)
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Star (game theory)
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