共查询到20条相似文献,搜索用时 15 毫秒
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For 0<p<∞ and α>−1, we let denote the space of those functions f which are analytic in the unit disc and satisfy . In this paper we characterize the positive Borel measures μ in D such that , 0<p<q<∞. We also characterize the pointwise multipliers from to (0<p<q<∞) if p−2<α<p. In particular, we prove that if the only pointwise multiplier from to (0<p<q<∞) is the trivial one. This is not longer true for and we give a number of explicit examples of functions which are multipliers from to for this range of values. 相似文献
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V. L. Oleînik 《Journal of Mathematical Sciences》2000,101(3):3133-3138
Let {
}, where {
} is the open unit disk on the complex plane {
}. In G, we consider analytic solutions u(t, z) ({
}, {
}) of the heat equation 2ut=uzz with initial data f(z)=u(0, z) belonging to the Fock space F, i.e., to the space of entire functions square summable with
the weight e−|z|2.Conditions on a nonnegative measure μ on G are described under which for all f ∈ F we have {
} Bibliography: 17 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 146–155.
Translated by S. V. Kislyakov. 相似文献
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Characterizations of bounded mean oscillation on the polydisk in terms of Hankel operators and Carleson measures 总被引:4,自引:0,他引:4
A scale of BMO spaces appears naturally in product spaces corresponding to the different, yet equivalent, characterizations
of the class of functions of bounded mean oscillation in one variable. S.-Y. Chang and R. Fefferman characterized product
BMO, the dual of the (real) Hardy spaceH
Re
1
on product domains, in terms of Carleson measures. Here we describe two other BMO spaces, one contained in and the other
containing product BMO, in terms of Carleson measures and Hankel operators. Both of these spaces play a significant role in
harmonic analysis of the polydisk and in multivariable operator theory.
First author supported in part by a grant from the National Science Foundation. Second author supported in part by a grant
from the Department of Energy. 相似文献
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Science China Mathematics - We study the relation between the boundary of a simply connected domain Ω being Ahlfors-regular and the invariance of Carleson measures under the push-forward... 相似文献
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Yong Jiao 《Probability Theory and Related Fields》2009,145(3-4):421-434
We study the relationship between vector-valued BMO martingales and Carleson measures. Let ${(\Omega,\mathcal {F} ,P)}$ be a probability space and 2 ≤ q < ∞. Let X be a Banach space. Given a stopping time τ, let ${\widehat{\tau}}$ denote the tent over τ: $$\widehat{\tau}=\{(w,k)\in \Omega\times \mathbb {N}: \tau(w)\leq k, \tau(w) < \infty\}.$$ We prove that there exists a positive constant c such that $$\sup_{\tau}\frac{1}{P(\tau < \infty)}\int \limits_{{\widehat{\tau}}}\|df_k\|^qdP\otimes dm\leq c^q\|f\|_{BMO(X)}^q$$ for any finite martingale with values in X iff X admits an equivalent norm which is q-uniformly convex. The validity of the converse inequality is equivalent to the existence of an equivalent p-uniformly smooth norm. And then we also give a characterization of UMD Banach lattices. 相似文献
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A. M. Sidorov 《Journal of Mathematical Sciences》1995,74(5):1283-1289
Translated fromIssledovaniya po Prikladnoi Matematike, No. 19, 1992, pp. 126–136. 相似文献
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S. Yu. Sadov 《Mathematical Notes》2013,94(3-4):551-558
It is shown that the Laplace transform of an L p (1 < p ≤ 2) function defined on the positive semiaxis satisfies the Hausdorff-Young type inequality with a positive weight in the right complex half-plane if and only if the weight is a Carleson measure. In addition, Carleson’s weighted L p inequality for the harmonic extension is given with a numeric constant. 相似文献
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In this paper, the so-called(p, φ)-Carleson measure is introduced and the relationship between vector-valued martingales in the general Campanato spaces Lp,φ(X) and the(p, φ)-Carleson measures is investigated. Specifically, it is proved that for q ∈ [2, ∞), the measure dμ := ||dfk||~qdP ? dm is a(q, φ)-Carleson measure on ? × N for every f ∈ L_q,φ(X)if and only if X has an equivalent norm which is q-uniformly convex; while for p ∈(1, 2], the measure dμ :=||dfk||~pdP ? dm is a(p, φ)-Carleson measure on ? × N implies that f ∈ L_p,φ(X)if and only if X admits an equivalent norm which is p-uniformly smooth. This result extends an earlier result in the literature from BMO spaces to general Campanato spaces. 相似文献
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Rauno Aulaskari Hasi Wulan Ruhan Zhao 《Proceedings of the American Mathematical Society》2000,128(8):2329-2335
For let be the Möbius transformation defined by , and let be the Green's function of the unit disk . We construct an analytic function belonging to for all , , but not belonging to meromorphic in and for any , . This gives a clear difference as compared to the analytic case where the corresponding function spaces ( and ) are same.
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Let 1 ≤ p < ∞ and let μ be a finite positive Borel measure on the unit disk D. The area Nevanlinna-Lebesgue space N
p
(μ) consists of all measurable functions h on D such that log+ |h| ∈ L
p
(μ), and the area Nevanlinna space N
α
p
is the subspace consisting of all holomorphic functions, in N
p
((1−|z|2)α
dv(z)), where α > −1 and ν is area measure on D. We characterize Carleson measures for N
α
p
, defined to be those measures μ for which N
α
p
⊂ N
p
(μ). As an application, we show that the spaces N
α
p
are closed under both differentiation and integration. This is in contrast to the classical Nevanlinna space, defined by
integration on circles centered at the origin, which is closed under neither. Applications to composition operators and to
integral operators are also given.
The second author was supported in part by KRF-2004-015-C00019. 相似文献
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Olivia Constantin 《Journal of Mathematical Analysis and Applications》2010,365(2):668-682
We prove Carleson-type embedding theorems for weighted Bergman spaces with Békollé weights. We use this to study properties of Toeplitz-type operators, integration operators and composition operators acting on such spaces. In particular, we investigate the membership of these operators to Schatten class ideals. 相似文献
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Boundedness of maximal operators and potential operators on Carleson curves in Lebesgue spaces with variable exponent 总被引:1,自引:0,他引:1
We prove the boundedness of the maximal operator Mr in the spaces L^p(·)(Г,p) with variable exponent p(t) and power weight p on an arbitrary Carleson curve under the assumption that p(t) satisfies the log-condition on Г. We prove also weighted Sobolev type L^p(·)(Г, p) → L^q(·)(Г, p)-theorem for potential operators on Carleson curves. 相似文献
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H. Turgay Kaptanolu 《Journal of Functional Analysis》2007,250(2):483-520
Carleson and vanishing Carleson measures for Besov spaces on the unit ball of are characterized in terms of Berezin transforms and Bergman-metric balls. The measures are defined via natural imbeddings of Besov spaces into Lebesgue classes by certain combinations of radial derivatives. Membership in Schatten classes of the imbeddings is considered too. Some Carleson measures are not finite, but the results extend and provide new insight to those known for weighted Bergman spaces. Special cases pertain to Arveson and Dirichlet spaces, and a unified view with the usual Hardy-space Carleson measures is presented by letting the order of the radial derivatives tend to 0. Weak convergence in Besov spaces is also characterized, and weakly 0-convergent families are exhibited. Applications are given to separated sequences, operators of Forelli–Rudin type, gap series, characterizations of weighted Bloch, Lipschitz, and growth spaces, inequalities of Fejér–Riesz and Hardy–Littlewood type, and integration operators of Cesàro type. 相似文献
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Zhijian Wu 《Proceedings of the American Mathematical Society》1999,127(11):3243-3249
We establish a capacitary strong type estimate for Lipschitz space and characterize the related Carleson measures.