doubling weight
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2020 ◽  
Vol 126 (3) ◽  
pp. 519-539
Author(s):  
Juntao Du ◽  
Songxiao Li ◽  
Yecheng Shi

In this paper, we investigate the boundedness, compactness, essential norm and the Schatten class of weighted composition operators $uC_\varphi $ on Bergman type spaces $A_\omega ^p $ induced by a doubling weight ω. Let $X=\{u\in H(\mathbb{D} ): uC_\varphi \colon A_\omega ^p\to A_\omega ^p\ \text {is bounded}\}$. For some regular weights ω, we obtain that $X=H^\infty $ if and only if ϕ is a finite Blaschke product.



Author(s):  
Carme Cascante ◽  
Joaquin M. Ortega

We give characterizations of the positive Borel measures μ on $\mathbb{S}^n$ so that the weighted Hardy–Sobolev spaces $H_s^p(w)$ are imbedded in Lq(dμ), for a range of s > 0, 0 < p, q < + ∞, q ≠ p, where w is a doubling weight in the unit sphere of ℂn.



2006 ◽  
Vol 58 (3) ◽  
pp. 492-528 ◽  
Author(s):  
Seng-Kee Chua

AbstractWe extend the extension theorems to weighted Sobolev spaces on (ε, δ) domains with doubling weight w that satisfies a Poincaré inequality and such that w–1/p is locally Lp′. We also make use of the main theorem to improve weighted Sobolev interpolation inequalities.





1996 ◽  
Vol 48 (3) ◽  
pp. 527-541 ◽  
Author(s):  
Seng-Kee Chua

AbstractWe study density and extension problems for weighted Sobolev spaces on bounded (ε, δ) domains𝓓when a doubling weight w satisfies the weighted Poincaré inequality on cubes near the boundary of 𝓓 and when it is in the MuckenhouptApclass locally in 𝓓. Moreover, when the weightswi(x) are of the form dist(x,Mi)αi,αi∈ ℝ,Mi⊂ 𝓓that are doubling, we are able to obtain some extension theorems on (ε, ∞) domains.



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