Bergman projection induced by radial weight

Peláez, José Ángel; Rättyä, Jouni

doi:10.1016/j.aim.2021.107950

Cited by 45 publications

(62 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…provided ω P D, by [17]. Our embedding theorem generalizes the case n " 0 of [11,Theorem 1] to doubling weights and reads as follows.…”

Section: Introduction and Main Resultsmentioning

confidence: 97%

See 1 more Smart Citation

Compact differences of composition operators on Bergman spaces induced by doubling weights

Liu¹,

Rättyä²,

Wu³

2020

Preprint

Self Cite

View full text Add to dashboard Cite

Bounded and compact differences of two composition operators acting from the weighted Bergman space A p ω to the Lebesgue space L q ν , where 0 ă q ă p ă 8 and ω belongs to the class D of radial weights satisfying a two-sided doubling condition, are characterized. On the way to the proofs a new description of q-Carleson measures for A p ω , with p ą q and ω P D, 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 α with ´1 ă α ă 8 to the setting of doubling weights. The case ω P p D is also briefly discussed and an open problem concerning this case is posed.

show abstract

“…provided ω P D, by [17]. Our embedding theorem generalizes the case n " 0 of [11,Theorem 1] to doubling weights and reads as follows.…”

Section: Introduction and Main Resultsmentioning

confidence: 97%

“…The intersection p D X q D is denoted by D, and this is the class of weights that we mainly work with. For recent developents on Bergman spaces induced by weights in p D, see [17] and the reference therein.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Compact differences of composition operators on Bergman spaces induced by doubling weights

Liu¹,

Rättyä²,

Wu³

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…A radial weight ρ is regular if ρ(r) ≍ (1 − r)ρ(r), r ∈ (0, 1). Recently, in 2019, they extended these results to the case where ρ 1 ∈ D, ρ 2 is radial [8].…”

Section: Van An Lementioning

confidence: 94%

“…Bounded analytic projections can also be used to establish duality relations and to obtain useful equivalent norms in spaces of analytic functions. Hence the boundedness of projections is an interesting topic which has been studied by many authors in recent years [1,2,3,7,8]. In [7], Peláez and Rättyä considered the projection P ρ 1 acting on L p ρ 2 (D), 1 ≤ p < ∞, when two weights ρ 1 , ρ 2 are in the class R of so called regular weights.…”

Section: Van An Lementioning

confidence: 99%

On the Bergman projections acting on $L^\infty$ in the unit ball $\mathbb B_n$

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…In this note, we study class D of so-called two-sided doubling weights, which originates from the work of J. A. Peláez and J. Rättyä [19,20]. For the definition of D we have to define two wider classes.…”

Section: Introduction and Characterizationsmentioning

confidence: 99%

Besov Spaces Induced by Doubling Weights

Reijonen

2020

Constr Approx

View full text Add to dashboard Cite

Let 1 ď p ă 8, 0 ă q ă 8 and ν be a two-sided doubling weight satisfying sup 0ďră1 p1´rq q ş 1 r νptq dt ż r 0 νpsq p1´sq q ds ă 8. The weighted Besov space B p,q ν consists of those f P H p such that ż 1 0ˆż 2π 0 |f 1 pre iθ q| p dθ˙q {p νprq dr ă 8.Our main result gives a characterization for f P B p,q ν depending only on |f |, p, q and ν. As a consequence of the main result and inner-outer factorization, we obtain several interesting by-products. For instance, we show the following modification of a classical factorization by F. and R. Nevanlinna: If f P B p,q ν , then there exist f1, f2 P B p,q ν X H 8 such that f " f1{f2. Moreover, we give a sufficient and necessary condition guaranteeing that the product of f P H p and an inner function belongs to B p,q ν . Applying this result, we make some observations on zero sets of B p,p ν .

show abstract

Bergman projection induced by radial weight

Cited by 45 publications

References 23 publications

Compact differences of composition operators on Bergman spaces induced by doubling weights

Compact differences of composition operators on Bergman spaces induced by doubling weights

On the Bergman projections acting on $L^\infty$ in the unit ball $\mathbb B_n$

Besov Spaces Induced by Doubling Weights

Contact Info

Product

Resources

About