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On some spaces of holomorphic functions of exponential growth on a half-plane

Marco M. Peloso, Maura Salvatori (2016)

Concrete Operators

In this paper we study spaces of holomorphic functions on the right half-plane R, that we denote by Mpω, whose growth conditions are given in terms of a translation invariant measure ω on the closed half-plane R. Such a measure has the form ω = ν ⊗ m, where m is the Lebesgue measure on R and ν is a regular Borel measure on [0, +∞). We call these spaces generalized Hardy–Bergman spaces on the half-plane R. We study in particular the case of ν purely atomic, with point masses on an arithmetic progression...

On some structural properties of Banach function spaces and boundedness of certain integral operators

T. S. Kopaliani (2004)

Czechoslovak Mathematical Journal

In this paper the notions of uniformly upper and uniformly lower -estimates for Banach function spaces are introduced. Further, the pair ( X , Y ) of Banach function spaces is characterized, where X and Y satisfy uniformly a lower -estimate and uniformly an upper -estimate, respectively. The integral operator from X into Y of the form K f ( x ) = ϕ ( x ) 0 x k ( x , y ) f ( y ) ψ ( y ) d y is studied, where k , ϕ , ψ are prescribed functions under some local integrability conditions, the kernel k is non-negative and is assumed to satisfy certain additional...

On some subspaces of Morrey-Sobolev spaces and boundedness of Riesz integrals

Mouhamadou Dosso, Ibrahim Fofana, Moumine Sanogo (2013)

Annales Polonici Mathematici

For 1 ≤ q ≤ α ≤ p ≤ ∞, ( L q , l p ) α is a complex Banach space which is continuously included in the Wiener amalgam space ( L q , l p ) and contains the Lebesgue space L α . We study the closure ( L q , l p ) c , 0 α in ( L q , l p ) α of the space of test functions (infinitely differentiable and with compact support in d ) and obtain norm inequalities for Riesz potential operators and Riesz transforms in these spaces. We also introduce the Sobolev type space W ¹ ( ( L q , l p ) α ) (a subspace of a Morrey-Sobolev space, but a superspace of the classical Sobolev space W 1 , α ) and obtain...

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