Integral means of δ-subharmonic functions and classes of entirely regular growth

Classes of functions of finite -type -subharmonic in m are investigated. A membership criterion that defines when a function belongs to the class expressed in terms of its integral q-means is established. Classes of entirely regular growth of functions that are -subharmonic in ^m are introduced and the behavior of these functions at infinity and the distribution of Riesz-associated measures are studied.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 3, pp. 408–416, March, 1992.     

An application of weighted Hardy spaces to the Navier–Stokes equations

In this article, we consider the mapping properties of convolution operators with smooth functions on weighted Hardy spaces H^p(w)$H^p(w)$ with w   belonging to Muckenhoupt class _A∞$A_{\infty }$. As a corollary, one obtains decay estimates of heat semigroup on weighted Hardy spaces. After a weighted version of the div–curl lemma is established, these estimates on weighted Hardy spaces are applied to the investigation of the decay property of global mild solutions to Navier–Stokes equations with the initial data belonging to weighted Hardy spaces.     

Integral representations and holonomic q-difference structure of Askey–Wilson type functions

We derive in a unified way the difference equations for Askey–Wilson polynomials and their Stieltjes transforms, by using basic properties of the de Rham cohomology associated with q-integral representations (Jackson integrals of BC ₁ type) of these functions.     

Closures of Hardy and Hardy–Sobolev Spaces in the Bloch Type Space on the Unit Ball

For \(0<\alpha <\infty \), \(0<p<\infty \) and \(0<s<\infty \), we characterize the closures in the \(\alpha \)-Bloch norm of \(\alpha \)-Bloch functions that are in a Hardy space \(H^p\) and in a Hardy–Sobolev space \(H^p_s\) on the unit ball of \(\mathbb {C}^n\).     

Hardy空间中的Bloch函数

本文利用单位圆盘内解析函数的Ｓｈｉｍｉｚｕ－Ａｈｌｆｏｒｓ特征函数分给出了Ｈａｒｄｙ空间中Ｂｌｏｃｈ函数和ＢＭＯＡ的新特征。由此我们发现了Ｂ∩Ｈ^ｐ（０＜ｐ＜∞）与ＢＭＯＡ之间的本质差别。     

The Bloch–Okounkov correlation functions at higher levels

We establish an explicit formula for the n-point correlation functions in the sense of Bloch–Okounkov for the irreducible representations of gl and of W_{1 +} arbitrary positive integral levels.     

Noncommutative Orlicz–Hardy spaces associated with growth functions

In this paper, we first present several basic properties of growth functions, and then prove a Hölder type inequality on noncommutative Orlicz spaces associated with a growth function. Moreover, we prove Riesz and Szegö type factorization theorems and the contractivity of the conditional expectation on noncommutative Orlicz–Hardy spaces associated with a growth function.     

Strong Hardy–Littlewood theorems for analytic functions and mappings of finite distortion

A formula is pointed out that explains why an analytic function often enjoys the same smoothness properties as its modulus. This is extended to quasiregular mappings and, mutatis mutandis, to mappings of finite distortion.Mathematics Subject Classification (1991): 30C65, 30D50, 30D55Supported in part by Grant 02-01-00267 from the Russian Foundation for Fundamental Research, DGICYT Grant BFM2002-04072-C02-01, CIRIT Grant 2001-SGR-00172, by the Ramón y Cajal program (Spain) and by the European Communitys Human Potential Program under contract HPRN-CT-2000-00116 (Analysis and Operators).     

Almost everywhere convergence of sequences of two-dimensional Walsh–Fejér means of integrable functions

The aim of this paper is to prove the a.e. convergence of sequences of the Fejér means of the Walsh–Fourier series of bivariate integrable functions. That is, let \(a = (a_{1}, a_{2})\:\mathbb{N} \to \mathbb{N}^{2}\) such that a _j (n+1)≧δsup _k≦n a _j (n) (j=1,2, n∈?) for some δ>0 and a ₁(+∞)=a ₂(+∞)=+∞. Then for each integrable function f∈L ¹(I ²) we have the a.e. relation \(\lim_{n\to\infty}\sigma_{a_{1}(n), a_{2}(n)}f = f\). It will be a straightforward and easy consequence of this result the cone restricted a.e. convergence of the two-dimensional Walsh–Fejér means of integrable functions which was proved earlier by the author and Weisz [3,8].     

Asymptotic radial symmetry and growth estimates of positive solutions to weighted Hardy–Littlewood–Sobolev system of integral equations

In this article, we study the asymptotics of the positive solutions of the Euler–Lagrange system of the weighted Hardy–Littlewood–Sobolev in R ⁿ $$\begin{array}{ll} u(x) = \frac{1}{|x|^{\alpha}}\int\limits_{R^{n}} \frac{v(y)^q}{|y|^{\beta}|x-y|^{\lambda}} dy,\\ v(x) = \frac{1}{|x|^{\beta}}\int\limits_{R^{n}} \frac{u(y)^p}{|y|^{\alpha}|x-y|^{\lambda}} dy.\end{array}$$ A new iterative method is introduced to obtain the optimal weighted local integrability of u(x). By this new method, we establish the asymptotic estimates of the solutions around the origin and near infinity. With these new estimates, we complete the study of the asymptotic behavior of the solutions. We believe this new iterative method and the new type of the weighted local estimates can be used in many other cases.     

Halfconvex functions and equality of Daróczy–Páles conjugate means

Using some properties of halfconvex and halfconcave functions, we solve the equality problem for conjugate means introduced by Daróczy and Páles.     

Weighted Hardy Space and Weighted Norm Inequalities of the Area Integral

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Approximation of functions of Dirichlet class by Fejér means

For the Dirichlet classes D _p of holomorphic functions in the disk, we obtain the exact orders of best polynomial approximations and of upper bounds for deviations of Fejér means of Taylor series in the Hardy spaces H _p.