共查询到20条相似文献,搜索用时 233 毫秒
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In this article, we present a Schwarz lemma at the boundary for pluriharmonic mappings from the unit polydisk to the unit ball, which generalizes classical Schwarz lemma for bounded harmonic functions to higher dimensions. It is proved that if the pluriharmonic mapping f ∈ P(D~n, B~N) is C~(1+α) at z0 ∈ E_rD~n with f(0) = 0 and f(z_0) = ω_0∈B~N for any n,N ≥ 1, then there exist a nonnegative vector λ_f =(λ_1,0,…,λ_r,0,…,0)~T∈R~(2 n)satisfying λ_i≥1/(2~(2 n-1)) for 1 ≤ i ≤ r such that where z'_0 and w'_0 are real versions of z_0 and w_0, respectively. 相似文献
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In this paper, we study operator-theoretic properties of the compressed shift operators and on complements of submodules of the Hardy space over the bidisk . Specifically, we study Beurling-type submodules – namely submodules of the form for θ inner – using properties of Agler decompositions of θ to deduce properties of and on model spaces . Results include characterizations (in terms of θ) of when a commutator has rank n and when subspaces associated to Agler decompositions are reducing for and . We include several open questions. 相似文献
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François Apéry 《Comptes Rendus Mathematique》2010,348(9-10):479-482
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M. Burak Erdoğan Michael Goldberg William R. Green 《Journal of Functional Analysis》2018,274(7):2139-2161
Let be a Schrödinger operator on with real-valued potential V, and let . If V has sufficient pointwise decay, the wave operators are known to be bounded on for all if zero is not an eigenvalue or resonance. We show that if there is an s-wave resonance or an eigenvalue only at zero, then the wave operators are bounded on for . This result stands in contrast to results in higher dimensions, where the presence of zero energy obstructions is known to shrink the range of valid exponents p. 相似文献
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Soon-Mo Jung 《Applied Mathematics Letters》2011,24(8):1322-1325
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Nguyen Van THIN 《数学物理学报(B辑英文版)》2017,37(3):623-656
In 1996, C. C. Yang and P. C. Hu [8] showed that: Let f be a transcendental meromorphic function on the complex plane, and a = 0 be a complex number; then assume that n ≥ 2, n_1, ···, n_k are nonnegative integers such that n_1+ ··· + n_k ≥1; thus f~n(f′)~(n_1)···(f~(k))~(n_k)-a has infinitely zeros. The aim of this article is to study the value distribution of differential polynomial, which is an extension of the result of Yang and Hu for small function and all zeros of f having multiplicity at least k ≥ 2. Namely, we prove that f~n(f′)~(n_1)···(f~(k))~(n_k)-a(z)has infinitely zeros, where f is a transcendental meromorphic function on the complex plane whose all zeros have multiplicity at least k ≥ 2, and a(z) ≡ 0 is a small function of f and n ≥ 2, n_1, ···, n_k are nonnegative integers satisfying n1+ ··· + n k ≥1. Using it, we establish some normality criterias for a family of meromorphic functions under a condition where differential polynomials generated by the members of the family share a holomorphic function with zero points. The results of this article are supplement of some problems studied by J. Yunbo and G. Zongsheng [6], and extension of some problems studied X. Wu and Y.Xu [10]. The main result of this article also leads to a counterexample to the converse of Bloch's principle. 相似文献
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Let p be an odd prime, and let x be a primitive root of p. Suppose that we write the elements of as and that, wherever we evaluate , we always write it as one of Let be a terrace for . Then is said to be a logarithmic terrace if , defined by , is also a terrace for . We study properties of logarithmic terraces, in particular investigating terraces which are simultaneously logarithmic for two different primitive roots. 相似文献
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David Kalaj 《Advances in Mathematics》2012,231(1):213-242
Let , be a solution of the Poisson equation , , in the unit disk. We prove and with sharp constants and , for , , and . In addition, for , with sharp constants and , we show and . We also give an extension to smooth Jordan domains.These problems are equivalent to determining a precise value of the norm of the Cauchy transform of Dirichlet’s problem. 相似文献
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Soyeun Jung 《Journal of Differential Equations》2012,253(6):1807-1861
By working with the periodic resolvent kernel and the Bloch-decomposition, we establish pointwise bounds for the Green function of the linearized equation associated with spatially periodic traveling waves of a system of reaction–diffusion equations. With our linearized estimates together with a nonlinear iteration scheme developed by Johnson–Zumbrun, we obtain -behavior () of a nonlinear solution to a perturbation equation of a reaction–diffusion equation with respect to initial data in recovering and slightly sharpening results obtained by Schneider using weighted energy and renormalization techniques. We obtain also pointwise nonlinear estimates with respect to two different initial perturbations , and , , respectively, sufficiently small and sufficiently large, showing that behavior is that of a heat kernel. These pointwise bounds have not been obtained elsewhere, and do not appear to be accessible by previous techniques. 相似文献
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Jinhuan Wang Linghua Kong Sining Zheng 《Nonlinear Analysis: Real World Applications》2010,11(3):2136-2140
This paper deals with Cauchy problem to nonlinear diffusion with , () and Hölder continuous. A new phenomenon is observed that the critical Fujita exponent whenever . More precisely, the solution blows up under any nontrivial and nonnegative initial data for all . This result is then extended to a coupled system with localized sources as well as the cases with other nonlinearities. 相似文献
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Let e be a positive integer, p be an odd prime, , and be the finite field of q elements. Let . The graph is a bipartite graph with vertex partitions and , and edges defined as follows: a vertex is adjacent to a vertex if and only if and . If and , the graph contains no cycles of length less than eight and is edge-transitive. Motivated by certain questions in extremal graph theory and finite geometry, people search for examples of graphs containing no cycles of length less than eight and not isomorphic to the graph , even without requiring them to be edge-transitive. So far, no such graphs have been found. It was conjectured that if both f and g are monomials, then no such graphs exist. In this paper we prove the conjecture. 相似文献