A Radial Integrability Result Concerning Bounded Functions in Analytic Besov Spaces with Applications

Domínguez, Salvador; Girela, Daniel

doi:10.1007/s00025-020-01194-4

Cited by 2 publications

(3 citation statements)

References 19 publications

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“…This was proved in [12] using, among other facts, a decomposition theorem for Besov spaces and Khinchine's inequality. The authors of this paper gave in [5] a new proof using Theorem A. Next we are going to give a new proof Theroem D using Theorem 1.1.…”

Section: An Application Of Theorem 11 To Multipliersmentioning

confidence: 99%

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Radial growth of the derivatives of analytic functions in Besov spaces

Domínguez

Girela

2020

Concrete Operators

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For 1 < p < ∞, the Besov space Bp consists of those functions f which are analytic in the unit disc 𝔻 = {z ∈ 𝔺 : |z| < 1} and satisfy ∫𝔻(1 − |z|2)p−2|f ′(z)|p dA(z) < ∞. The space B2 reduces to the classical Dirichlet space 𝒟. It is known that if f ∈ 𝒟then |f ′(reiθ)| = o[(1 − r)−1/2], for almost every ∈ [0, 2π]. Hallenbeck and Samotij proved that this result is sharp in a very strong sense. We obtain substitutes of the above results valid for the spaces Bp (1 < p < ∞) an we give also an application of our them to questions concerning multipliers between Besov spaces.

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Section: An Application Of Theorem 11 To Multipliersmentioning

confidence: 99%

“…Theorem A was applied in [5] to obtain results on multipliers and superposition operators acting on Besov spaces. Our aim in this work is to obtain sharp estimates on the growth of the derivatives of B p -functions on "almost every radius".…”

Section: Introductionmentioning

confidence: 99%

Radial growth of the derivatives of analytic functions in Besov spaces

Domínguez

Girela

2020

Concrete Operators

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“…For the analytic corresponding classes of Besov spaces, we cite [2][3][4][5][6][7]. In this article, the general meromorphic Besov-type classes always refer to the concerned classes B # (q, q − 2, s; n).…”

Section: Introductionmentioning

confidence: 99%

On Some Classes with Norms of Meromorphic Function Spaces Defined by General Spherical Derivatives

Ahmed

2021

Journal of Mathematics

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The main concerned target of this article is to define and study some concerned classes of meromorphic function spaces using the general spherical derivatives. The general Besov-type classes of meromorphic functions as well as the general normal functions are considered intensively and both are compared deeply with each other. Specifically, multiple results concerning general meromorphic-type classes as well as non-normal classes are obtained by the help of general spherical derivatives. The concerned results are proved by constructing some specific mild conditions on the sequences of points belonging to the concerned meromorphic-type classes. The obtained results generalize and improve the corresponding previous results in some concerned respects. The concerned proofs and methods are simply presented.

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A Radial Integrability Result Concerning Bounded Functions in Analytic Besov Spaces with Applications

Abstract: We prove that for every p ≥ 1 there exists a bounded function in the analytic Besov space B p whose derivative is "badly integrable" along every radius. We apply this result to study multipliers and weighted superposition operators acting on the spaces B p .

Cited by 2 publications

References 19 publications

Radial growth of the derivatives of analytic functions in Besov spaces

Radial growth of the derivatives of analytic functions in Besov spaces

On Some Classes with Norms of Meromorphic Function Spaces Defined by General Spherical Derivatives

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