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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2020-12-01
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| Series: | Concrete Operators |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/conop-2020-0107 |
| _version_ | 1819093810575048704 |
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| author | Domínguez Salvador Girela Daniel |
| author_facet | Domínguez Salvador Girela Daniel |
| author_sort | Domínguez Salvador |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-21T23:17:26Z |
| format | Article |
| id | doaj.art-75d4de55695544a1bbfe4268f57ac0cf |
| institution | Directory Open Access Journal |
| issn | 2299-3282 |
| language | English |
| last_indexed | 2024-12-21T23:17:26Z |
| publishDate | 2020-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Concrete Operators |
| spelling | doaj.art-75d4de55695544a1bbfe4268f57ac0cf2022-12-21T18:46:53ZengDe GruyterConcrete Operators2299-32822020-12-018111210.1515/conop-2020-0107conop-2020-0107Radial growth of the derivatives of analytic functions in Besov spacesDomínguez Salvador0Girela Daniel1Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071Málaga, SpainAnálisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071Málaga, SpainFor 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.https://doi.org/10.1515/conop-2020-0107besov spacesradial behaviourmultipliers30h2547b38 |
| spellingShingle | Domínguez Salvador Girela Daniel Radial growth of the derivatives of analytic functions in Besov spaces Concrete Operators besov spaces radial behaviour multipliers 30h25 47b38 |
| title | 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_short | Radial growth of the derivatives of analytic functions in Besov spaces |
| title_sort | radial growth of the derivatives of analytic functions in besov spaces |
| topic | besov spaces radial behaviour multipliers 30h25 47b38 |
| url | https://doi.org/10.1515/conop-2020-0107 |
| work_keys_str_mv | AT dominguezsalvador radialgrowthofthederivativesofanalyticfunctionsinbesovspaces AT gireladaniel radialgrowthofthederivativesofanalyticfunctionsinbesovspaces |