Carleson measures and reproducing kernel thesis in Dirichlet-type spaces
نویسندگان
چکیده
منابع مشابه
Carleson Measures on Dirichlet-type Spaces
We show that a maximal inequality holds for the non-tangential maximal operator on Dirichlet spaces with harmonic weights on the open unit disc. We then investigate two notions of Carleson measures on these spaces and use the maximal inequality to give characterizations of the Carleson measures in terms of an associated capacity.
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We give a necessary and sufficient condition for a measure μ in the closed unit disk to be a reverse Carleson measure for Hardy spaces. This extends a previous result of Lefèvre, Li, Queffélec and Rodrı́guez-Piazza [LLQR]. We also provide a simple example showing that the analogue for the Paley-Wiener space does not hold. As it turns out the analogue never holds in any model space.
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P (α) = C(α, F (x, y)) = αF (x, x) + 2αF (x, y) + F (x, y)F (y, y), which is ≥ 0. In the case F (x, x) = 0, the fact that P ≥ 0 implies that F (x, y) = 0. In the case F (x, y) 6= 0, P (α) is a quadratic polynomial and because P ≥ 0 it follows that the discriminant of P is ≤ 0: 4F (x, y) − 4 · F (x, x) · F (x, y)F (y, y) ≤ 0. That is, F (x, y) ≤ F (x, y)F (x, x)F (y, y), and this implies that F ...
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ژورنال
عنوان ژورنال: St. Petersburg Mathematical Journal
سال: 2013
ISSN: 1061-0022,1547-7371
DOI: 10.1090/s1061-0022-2013-01269-6