共查询到20条相似文献,搜索用时 31 毫秒
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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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Anuj Jakhar Sudesh K. Khanduja Neeraj Sangwan 《Journal of Pure and Applied Algebra》2018,222(4):889-899
Let v be a Krull valuation of a field with valuation ring . Let θ be a root of an irreducible trinomial belonging to . In this paper, we give necessary and sufficient conditions involving only for to be integrally closed. In the particular case when v is the p-adic valuation of the field of rational numbers, and , then it is shown that these conditions lead to the characterization of primes which divide the index of the subgroup in , where is the ring of algebraic integers of K. As an application, it is deduced that for any algebraic number field K and any quadratic field L not contained in K, we have if and only if the discriminants of K and L are coprime. 相似文献
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刘岚喆 《数学物理学报(B辑英文版)》2005,25(1):89-94
It is proved that, for the nondivergence elliptic equations ∑in, j=1 aijuxixj = f,if f belongs to the generalized Morrey spaces Lp,ψ(ω), then uxixj ∈ Lp,ψ(ω), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp,ψ (ω). 相似文献
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Let p be a prime and let be a primitive p-th root of unity. For a finite extension k of containing , we consider a Kummer extension of degree p. In this paper, we show that if and the class number of k is one, the index of is one. We also show that if is tamely ramified with a normal integral basis, the index is at most a power of p. In the last section, we show that there exist infinitely many cubic Kummer extensions of for both wildly and tamely ramified cases, whose integer rings do not have a power integral basis over that of . 相似文献
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Christoph Brause Arnfried Kemnitz Massimiliano Marangio Anja Pruchnewski Margit Voigt 《Discrete Mathematics》2017,340(11):2633-2640
Let be a simple graph and for every vertex let be a set (list) of available colors. is called -colorable if there is a proper coloring of the vertices with for all . A function is called a choice function of and is said to be -list colorable if is -colorable for every list assignment choice function is defined by and the sum choice number
denotes the minimum size of a choice function of .Sum list colorings were introduced by Isaak in 2002 and got a lot of attention since then.For a generalized
-graph is a simple graph consisting of two vertices and connected by internally vertex disjoint paths of lengths
.In 2014, Carraher et al. determined the sum-paintability of all generalized -graphs which is an online-version of the sum choice number and consequently an upper bound for it.In this paper we obtain sharp upper bounds for the sum choice number of all generalized -graphs with and characterize all generalized -graphs which attain the trivial upper bound . 相似文献
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A finite Borel measure μ in is called a frame-spectral measure if it admits an exponential frame (or Fourier frame) for . It has been conjectured that a frame-spectral measure must be translationally absolutely continuous, which is a criterion describing the local uniformity of a measure on its support. In this paper, we show that if any measures ν and λ without atoms whose supports form a packing pair, then is translationally singular and it does not admit any Fourier frame. In particular, we show that the sum of one-fourth and one-sixteenth Cantor measure does not admit any Fourier frame. We also interpolate the mixed-type frame-spectral measures studied by Lev and the measure we studied. In doing so, we demonstrate a discontinuity behavior: For any anticlockwise rotation mapping with , the two-dimensional measure , supported on the union of x-axis and , always admit a Fourier frame. Furthermore, we can find such that it forms a Fourier frame for with frame bounds independent of θ. Nonetheless, does not admit any Fourier frame. 相似文献
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The classic Rosenthal–Lacey theorem asserts that the Banach space of continuous real-valued maps on an infinite compact space K has a quotient isomorphic to c or . More recently, Ka?kol and Saxon [20] proved that the space endowed with the pointwise topology has an infinite-dimensional separable quotient algebra iff K has an infinite countable closed subset. Hence lacks infinite-dimensional separable quotient algebras. This motivates the following question: (?) Doesadmit an infinite-dimensional separable quotient (shortly SQ) for any infinite compact space K? Particularly, does admit SQ? Our main theorem implies that has SQ for any compact space K containing a copy of . Consequently, this result reduces problem (?) to the case when K is an Efimov space (i.e. K is an infinite compact space that contains neither a non-trivial convergent sequence nor a copy of ). Although, it is unknown if Efimov spaces exist in ZFC, we show, making use of some result of R. de la Vega (2008) (under ?), that for some Efimov space K the space has SQ. Some applications of the main result are provided. 相似文献
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Sergey V. Astashkin Pavel A. Terekhin 《Journal of Mathematical Analysis and Applications》2018,457(1):645-671
Let be a mean zero function and let , , be the dyadic dilations and translations of f. We investigate conditions on f, under which the linear operator defined by , , where , , are mean zero Haar functions, can be continuously extended to the closed linear span in a certain function space X. Among other results we prove that is bounded in every symmetric space with nontrivial Boyd indices whenever and f has “good” Haar spectral properties. In the special case of so-called Haar chaoses the above results can be essentially refined and sharpened. In particular, we find necessary and sufficient conditions, under which the operator , generated by a Haar chaos f of order 1, is continuously invertible in for all . 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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Ferenc Weisz 《Journal of Approximation Theory》2011,163(2):99-116
It is proved that the maximal operator of the -Fejér means of a -dimensional Fourier series is bounded from the periodic Hardy space to for all and, consequently, is of weak type (1, 1). As a consequence we obtain that the -Fejér means of a function converge a.e. to . Moreover, we prove that the -Fejér means are uniformly bounded on the spaces and so they converge in norm . Similar results are shown for conjugate functions and for a general summability method, called -summability. Some special cases of the -summation are considered, such as the Weierstrass, Picard, Bessel, Fejér, de la Vallée Poussin, Rogosinski and Riesz summations. 相似文献
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Tomoyuki Nakatsuka 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(8):3457-3464
The aim of this paper is to prove a uniqueness criterion for solutions to the stationary Navier–Stokes equation in 3-dimensional exterior domains within the class with , where and are the Lorentz spaces. Our criterion asserts that if and are the solutions, is small in and for some , then . The proof is based on analysis of the dual equation with the aid of the bootstrap argument. 相似文献