Radial growth of the derivatives of analytic functions in Besov spaces
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], f...
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De Gruyter
2020
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oai:doaj.org-article:75d4de55695544a1bbfe4268f57ac0cf2021-12-05T14:10:45ZRadial growth of the derivatives of analytic functions in Besov spaces2299-328210.1515/conop-2020-0107https://doaj.org/article/75d4de55695544a1bbfe4268f57ac0cf2020-12-01T00:00:00Zhttps://doi.org/10.1515/conop-2020-0107https://doaj.org/toc/2299-3282For 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.Domínguez SalvadorGirela DanielDe Gruyterarticlebesov spacesradial behaviourmultipliers30h2547b38MathematicsQA1-939ENConcrete Operators, Vol 8, Iss 1, Pp 1-12 (2020) |
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DOAJ |
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DOAJ |
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EN |
| topic |
besov spaces radial behaviour multipliers 30h25 47b38 Mathematics QA1-939 |
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besov spaces radial behaviour multipliers 30h25 47b38 Mathematics QA1-939 Domínguez Salvador Girela Daniel Radial growth of the derivatives of analytic functions in Besov spaces |
| description |
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. |
| format |
article |
| author |
Domínguez Salvador Girela Daniel |
| author_facet |
Domínguez Salvador Girela Daniel |
| author_sort |
Domínguez Salvador |
| title |
Radial growth of the derivatives of analytic functions in Besov spaces |
| title_short |
Radial growth of the derivatives of analytic functions in Besov spaces |
| title_full |
Radial growth of the derivatives of analytic functions in Besov spaces |
| title_fullStr |
Radial growth of the derivatives of analytic functions in Besov spaces |
| title_full_unstemmed |
Radial growth of the derivatives of analytic functions in Besov spaces |
| title_sort |
radial growth of the derivatives of analytic functions in besov spaces |
| publisher |
De Gruyter |
| publishDate |
2020 |
| url |
https://doaj.org/article/75d4de55695544a1bbfe4268f57ac0cf |
| work_keys_str_mv |
AT dominguezsalvador radialgrowthofthederivativesofanalyticfunctionsinbesovspaces AT gireladaniel radialgrowthofthederivativesofanalyticfunctionsinbesovspaces |
| _version_ |
1718371764093845504 |