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The measure of non-compactness is estimated from below for various operators, including the Hardy--Littlewood maximal opera\-tor, the fractional maximal operator and the Hilbert transform, all acting ...
Let $\mu$ be a non-negative Radon measure on ${\mathbb R}^d$ which satisfies only some growth conditions. Under this assumption, the boundedness in some Hardy-type spaces is established for a class of...
In this work, we prove that a map $F$ from a compact metric space $K$ into a Banach space $X$ over ${\Bbb F}$ is a Lipschitz-$\alpha$ operator if and only if for each $\sigma$ in $X^*$ the map $\sigma...
In this work we study the spectral counting function for the $p$-Laplace operator in one dimension. We show the existence of a two-term Weyl-type asymptote. The method of proof is rather elementary, b...
We consider a pair of Hamiltonians $(H, H_0 )$ on $L^2 ({\Bbb R}^n ),$ where $H_0 = p^2 -x^2$ is a Schr\" odinger operator with a repulsive potential, and $H= H_0 +V(x)$. We show that, under suitable ...
In this paper, we investigate the relation between the rate of convergence for the derivatives of the combinations of Baskakov operators and the smoothness for the derivatives of the functions approxi...
Let $u$ be a solution to a second order elliptic equation with singular potentials belonging to Kato--Fefferman--Phong's class in Lipschitz domains. An elementary proof of the doubling property for $u...
We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type $(1,1)$ inequalities. As an applicat...
Let ${\mathscr H}$ be a complex seperable Hilbert space and ${\mathscr L}({\mathscr H})$ denote the collection of bounded linear operators on ${\mathscr H}$. For an operator in ${\mathscr L}% ({\maths...
In the present paper, a problem of Ioana Mihaila is negatively answered on the invertibility of composition operators on Riemann surfaces, and it is proved that the composition operator $C_{\rho }$ is...
设(G,G+)为一个拟格序群,H为G+的可传定向子集.令GN=G+·H^-1,F^GN为相应的Toeputz算子代数.作者刻划了F^GN的忠实表示。
设G为一离散交换群,(G,G+)为一拟偏序群.相应于这样的一个拟偏序群(G,G+),构造了一个万有Toeplitz算子代数.
We introduce two K-theories, one for vector bundles whose fibers are modules of vertex operator algebras, another for vector bundles whose fibers are modules of associative algebras. We verify the coh...
The purpose of this paper is to obtain the estimate for the average mean value of the remainder term of the asymptotic formula for the quadratic mean value of the Fourier coefficients of the eigenfunc...
We obtain a generalization of the ideal {\cal M}(q,p) of (q,p)-mixing operators-in the sense of Pietsch- as a consequence of the study of the quotients of (p, s)-absolutely continuous operator ideals ...

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