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

Labor markets have the three R functions of recruiting workers, remunerating them to encourage them to perform their jobs satisfactorily, and retaining experienced and productive workers. Employers in one country and jobs in another complicate these three Rs, especially recruitment, which is why both employers and workers often turn to private recruiters to act as intermediaries between jobs and workers. Recruiters are most deeply involved in the second phase of the four-phase labor migration process—matching workers with jobs. Indeed, the fact that recruiters rarely visit the workplaces to which they send workers, and do not always expect to send more workers to particular employers, reduces their incentives to make good worker–job matches.

Download Full-text

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

Journal of Geometric Analysis ◽

10.1007/s12220-021-00724-y ◽

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.

Download Full-text

Hardy Spaces for Quasiregular Mappings and Composition Operators

Journal of Geometric Analysis ◽

10.1007/s12220-021-00687-0 ◽

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).

Download Full-text