A remark on Carleson measures of domains in ℂⁿ

2021 ◽  
Author(s):  
Phung Thuc
Keyword(s):  
Carleson Measures

scholarly journals Compact Differences of Composition Operators on Bergman Spaces Induced by Doubling Weights

2021 ◽  
Author(s):  
Bin Liu ◽  
Jouni Rättyä ◽  
Fanglei Wu
Keyword(s):  
Bergman Space ◽  
Open Problem ◽  
Lebesgue Space ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Carleson Measures ◽  
Doubling Weights ◽  
The Way

AbstractBounded and compact differences of two composition operators acting from the weighted Bergman space $$A^p_\omega $$ A ω p to the Lebesgue space $$L^q_\nu $$ L ν q , where $$0<q<p<\infty $$ 0 < q < p < ∞ and $$\omega $$ ω belongs to the class "Equation missing" of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proofs a new description of q-Carleson measures for $$A^p_\omega $$ A ω p , with $$p>q$$ p > q and "Equation missing", involving pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of q-Carleson measures for the classical weighted Bergman space $$A^p_\alpha $$ A α p with $$-1<\alpha <\infty $$ - 1 < α < ∞ to the setting of doubling weights. The case "Equation missing" is also briefly discussed and an open problem concerning this case is posed.

scholarly journals Hardy Spaces for Quasiregular Mappings and Composition Operators

2021 ◽  
Author(s):  
Tomasz Adamowicz ◽  
María J. González
Keyword(s):  
Hardy Spaces ◽  
Composition Operators ◽  
Quasiconformal Mappings ◽  
Carleson Measures ◽  
Quasiregular Mappings ◽  
Classical Setting ◽  
Appl Math ◽  
Analytic Mappings

AbstractWe define Hardy spaces $${\mathcal {H}}^p$$ H p for quasiregular mappings in the plane, and show that for a particular class of these mappings many of the classical properties that hold in the classical setting of analytic mappings still hold. This particular class of quasiregular mappings can be characterised in terms of composition operators when the symbol is quasiconformal. Relations between Carleson measures and Hardy spaces play an important role in the discussion. This program was initiated and developed for Hardy spaces of quasiconformal mappings by Astala and Koskela in 2011 in their paper $${\mathcal {H}}^p$$ H p -theory for Quasiconformal Mappings (Pure Appl Math Q 7(1):19–50, 2011).

Carleson measures and the generalized Campanato spaces of vector-valued martingales

2018 ◽  
Vol 38 (6) ◽  
pp. 1779-1788
Author(s):  
Lin YU ◽  
Ruhui WANG ◽  
Shoujiang ZHAO
Keyword(s):  
Carleson Measures ◽  
Vector Valued

Odd BMO $${(\mathbb{R})}$$ Functions and Carleson Measures in the Bessel Setting

2010 ◽  
Vol 66 (4) ◽  
pp. 463-494 ◽  
Author(s):  
J. J. Betancor ◽  
A. Chicco Ruiz ◽  
J. C. Fariña ◽  
L. Rodríguez-Mesa
Keyword(s):  
Carleson Measures ◽  
R Functions

K-Carleson Measures

2017 ◽  
pp. 81-117
Author(s):  
Hasi Wulan ◽  
Kehe Zhu
Keyword(s):  
Carleson Measures

BMO(ρ) and Carleson Measures

1985 ◽  
Vol 287 (1) ◽  
pp. 107 ◽  
Author(s):  
Wayne Stewart Smith
Keyword(s):  
Carleson Measures
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