Embedding theorems and integration operators on Bergman spaces with rapidly decreasing weights
By Jordi Pau, J. A. Pel'aez. 2010
100 citations recorded by the source corpus.
We completely describe those positive Borel measures μ in the unit disc D such that the Bergman space Ap(w)⊂Lq(μ), 0 0, and some double exponential type weights. As an application of that result, we characterize the boundedness and the compactness of Tg:Ap(w)→Aq(w), 0<p,q<∞, w∈W, where Tg is the integration operator (Tgf)(z)=∫0zf(ζ)g′(ζ)dζ. The particular choice of the weight wα(r) answers an open question posed by A. Aleman and A. Siskakis. We also describe those analytic functions in D for which Tg belongs to the Schatten p-class of A2(w), 0<p<∞.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/a7d443c8aa23ce5013ac3e0de435dad5d8aaeea1
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In Applied Mathematics
Citations in the corpus
- Carleson Measures, Riemann–Stieltjes and Multiplication Operators on a General Family of Function Spaces (2013, unknown): “See, [1], [3], [13], [19], and [22] for a few examples.”
- A Volterra-type integration operator on Fock spaces (2012, unknown): “The boundedness and compactness, as well as some spectral properties (such as Schatten class membership) of Tg acting on various spaces of analytic functions of the unit disc D in C have been extensively investigated (see [2, 6] for Hardy spaces, [3, 5, 8, 17, 19] for weighted Bergman spaces, and [9”
- Integral Operators, Embedding Theorems and a Littlewood–Paley Formula on Weighted Fock Spaces (2013, methodology): “Analogues of Theorem 3 and Corollary 11 for the setting of Bergman spaces with rapidly decreasing weights were obtained in [19, 21].”
- Embedding theorems for Bergman spaces via harmonic analysis (2014, background): “The problem has also been solved for the Bekollé-Bonami and, if n = 0, the rapidly decreasing weights [6, 12].”
- Integration operators between Hardy spaces on the unit ball of $\Cn$ (2013, unknown): “After the pioneering works of Aleman, Siskakis and Cima [4, 6, 7] describing the boundedness and compactness of the operator Jg in Hardy and Bergman spaces, the mentioned operator became extremely popular, being studied in many spaces of analytic functions (see [4, 5, 6, 7, 13, 27, 28] for example).”
- Small weighted Bergman spaces (2015, methodology): “See [9, 8, 22, 23, 45, 46, 58] for progress on the theory of these spaces.”
- Weighted Bergman spaces induced by rapidly incresing weights (2012, methodology): “The membership of the integral operator Tg in the Schatten p-class Sp(H) has been characterized when H is either the Hardy spaceH(2) [10], the classical weighted Bergman space A(2)α [11], or the weighted Bergman space A 2 ω , where ω is a rapidly decreasing weight [64, 65] or a Bekollé-Bonami weight”
- Boundedness of the Bergman projection on $L^p$ spaces with exponential weights (2013, background): “Other similarities between Fock spaces and Bergman spaces with rapidly decreasing weights were pointed out in [12, 3].”