Embedding theorems for spaces of analytic functions via Khinchine's inequality.

Luecking, Daniel H.

doi:10.1307/mmj/1029004756

Cited by 124 publications

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“…) k is the Radmecher sequence of function on [0, 1] chosen as in [8], then the sequence (a k r k (t)) also belongs to ℓ p with (a k r k (t)) ℓ p = (a k ) ℓ p for all t. This implies that the function…”

Section: 2mentioning

confidence: 99%

“…It means that λI − D is injective whenever |λ| ≥ 1. On the other hand, for such values of λ, a simple computation again shows that the equation λf − Df = h has a unique analytic solution 8) where R λ is the resolvent operator of D at point λ, C = f (0) is a constant value. We remain to show that the operator R λ given by the explicit expression in (3.8) is bounded on F (m,p) .…”

Section: Part (Ii)mentioning

confidence: 99%

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A note on the differential operator on generalized Fock spaces

Mengestie

2018

Journal of Mathematical Analysis and Applications

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Abstract. It has long been known that the differential operator D represents a typical example of unbounded operators on many Banach spaces including the classical Fock spaces, the Fock-Sobolev spaces, and the generalized Fock spaces where the weight decays faster than the Gaussian weight. In this note we identify Fock type spaces where the operator admits boundedness, compactness and membership in the Schatten S p class spectral structures. We also showed that its nontrivial spectrum while acting on such spaces is precisely the closed unit disk D in the complex plane.

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Section: 2mentioning

confidence: 99%

Section: Part (Ii)mentioning

confidence: 99%

A note on the differential operator on generalized Fock spaces

Mengestie

2018

Journal of Mathematical Analysis and Applications

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“…To prove that (a) implies (c), we follow the proof of Theorem 1 in Luecking [38]. Let {a j } be the sequence of points in B n from Theorem 2.30 in [68].…”

Section: If the Functionmentioning

confidence: 99%

“…Let r j (t) be a sequence of Rademacher functions (see page 336 of Luecking [38]). If we replace c j by r j (t)c j , the above inequality is still true, so…”

Section: If the Functionmentioning

confidence: 99%

Theory of Bergman Spaces in the Unit Ball of C^n

Zhao¹,

Zhu²

2008

Mémoires Soc. Math. France

169

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ABSTRACT. There has been a great deal of work done in recent years on weighted Bergman spaces A p α on the unit ball B n of C n , where 0 < p < ∞ and α > −1. We extend this study in a very natural way to the case where α is any real number and 0 < p ≤ ∞. This unified treatment covers all classical Bergman spaces, Besov spaces, Lipschitz spaces, the Bloch space, the Hardy space H 2 , and the so-called Arveson space. Some of our results about integral representations, complex interpolation, coefficient multipliers, and Carleson measures are new even for the ordinary (unweighted) Bergman spaces of the unit disk.

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“…The q-Carleson measures for the space H p were characterized by Duren [14] in the case 0 < p < q < ∞, and by Luecking [28] in the case 0 < q < p < ∞ (see also the recent paper [9]). Luecking [26,29], characterized the q-Carleson measures for the space A p α , 0 < p, q < ∞. A good number of results about p-Carleson measures for Besov spaces and spaces of Dirichlet type of analytic functions have been obtained by different authors (see, e. g., [4], [5], [20], [21], [22], [33], [39], [42], [43], and [44]).…”

Section: S(i) = {Rementioning

confidence: 99%

Carleson Measures for the Bloch Space

Girela

Peláez

Pérez-González

et al. 2008

Integr. equ. oper. theory

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Abstract. In this paper we study the positive Borel measures µ on the unit disc D in C for which the Bloch space B is continuously included in L p (dµ), 0 < p < ∞. We call such measures p-Bloch-Carleson measures. We give two conditions on a measure µ in terms of certain logarithmic integrals one of which is a necessary condition and the other a sufficient condition for µ being a p-Bloch-Carleson measure. We also give a complete characterization of the p-Bloch-Carleson measures within certain special classes of measures. It is also shown that, for p > 1, the p-Bloch-Carleson measures are exactly those for which the Toeplitz operator T µ , defined by T µ (f )(z) =

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Embedding theorems for spaces of analytic functions via Khinchine's inequality.

Cited by 124 publications

References 0 publications

A note on the differential operator on generalized Fock spaces

A note on the differential operator on generalized Fock spaces

Theory of Bergman Spaces in the Unit Ball of C^n

Carleson Measures for the Bloch Space

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