共查询到20条相似文献,搜索用时 11 毫秒
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V. B. Korotkov 《Siberian Mathematical Journal》2018,59(4):677-680
We establish some algebraic, metric, and spectral properties of convolution integral operators in L2(?N). 相似文献
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C. AparicioA.R. Villena 《Journal of Functional Analysis》2002,196(1):155-161
Let G be a locally compact abelian group, let μ be a bounded complex-valued Borel measure on G, and let Tμ be the corresponding convolution operator on L1(G). Let X be a Banach space and let S be a continuous linear operator on X. Then we show that every linear operator Φ: X→L1(G) such that ΦS=TμΦ is continuous if and only if the pair (S,Tμ) has no critical eigenvalue. 相似文献
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We obtain (essentially sharp) boundedness results for certain generalized local maximal operators between fractional weighted Sobolev spaces and their modifications. Concrete boundedness results between well known fractional Sobolev spaces are derived as consequences of our main result. We also apply our boundedness results by studying both generalized neighbourhood capacities and the Lebesgue differentiation of fractional weighted Sobolev functions. 相似文献
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The purpose of this paper is to introduce a class of maximal monotone operators on Banach spaces that contains all maximal monotone operators on reflexive spaces, all subdifferential operators of proper, lsc, convex functions, and, more generally, all maximal monotone operators that verify the simplest possible sum theorem. Dually strongly maximal monotone operators are also contained in this class. We shall prove that if T is an operator in this class, then
(the norm closure of its domain) is convex, the interior of co(dom(T)) (the convex hull of the domain of T) is exactly the set of all points of
at which T is locally bounded, and T is maximal monotone locally, as well as other results. 相似文献
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Hypercyclic and Chaotic Convolution Operators 总被引:3,自引:0,他引:3
Every convolution operator on a space of ultradifferentiablefunctions of Beurling or Roumieu type and on the correspondingspace of ultradistributions is hypercyclic and chaotic whenit is not a multiple of the identity. The operator of differentiationis hypercyclic on the space A, but it need not be hypercyclicon radial weighted algebras of entire functions. 相似文献
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J. M. ALDAZ Juan L. VARONA 《数学学报(英文版)》2007,23(3):487-490
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 application, we prove that the best constants for the centered Hardy-Littlewood maximal operator associated with parallelotopes do not decrease with the dimension. 相似文献
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Hiro-O Kitax 《Mathematische Nachrichten》1998,193(1):57-74
Let S* (f be the majorant function of the partial sums of the trigonometric Fourier series of f. In this paper we consider the Orlicz space Lπ and give a generalization of Soria's result [S1]. Let π (t) be a concave function with some nice properties and . If there exists a positive constant a0 < 1 such that then we have . 相似文献
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We establish the connection between the boundedness of convolution operators on Hp(ℝN) and some related operators on Hp(ℤN). The results we obtain here extend the already known for Lp spaces with p > 1. We also study similar results for maximal operators given by convolution with the dilation of a fixed kernel. Our main tools are some known results about functions of exponential type already presented in [BC1] that, in particular, allow us to prove a sampling theorem for functions of exponential type belonging to Hardy spaces 相似文献
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Certain Convolution Operators for Meromorphic Functions 总被引:3,自引:0,他引:3
Dinggong Yang 《Southeast Asian Bulletin of Mathematics》2001,25(1):175-186
Let (p N) be the class of functions
analytic in 0 < |z| < 1. A convolution operator Lp(a, c) on p is introduced. This paper gives some sharp inequalities for f(z) satisfying Re{(1 – )zpLp(a, c) f(z) + zpLp(a + 1, c) f(z)} > , where 0, < 1, a > 0 and c 0, –1, –2,....AMS Subject Classification (1991) 30C45 30A10 相似文献
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The purpose of this paper is to establish connections between the class of maximal monotone operators of Br?ndsted–Rockafellar
type and that of regular maximal monotone operators.
†Partially supported by a WISE grant. 相似文献
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Andreas Löhne 《Set-Valued and Variational Analysis》2008,16(5-6):693-700
It is shown that a set-valued map $M:\mathbb{R}^{q} \rightrightarrows \mathbb{R}^{q}$ is maximal monotone if and only if the following five conditions are satisfied: (i) M is monotone; (ii) M has a nearly convex domain; (iii) M is convex-valued; (iv) the recession cone of the values M(x) equals the normal cone to the closure of the domain of M at x; (v) M has a closed graph. We also show that the conditions (iii) and (v) can be replaced by Cesari’s property (Q). 相似文献
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Carmen Fernndez 《Mathematische Nachrichten》2000,216(1):61-71
Let (ω)(ℝ) denote the non–quasianalytic class of Beurling type on ℝ. For μ, ν ∈ ′(ω)(ℝ) we give necessary conditions for the inclusion Tν( (ω)(ℝ)) ⊂ Tμ( (ω)(ℝ)), thus extending previous work of Malgrange and Ehrenpreis . 相似文献
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We study the behaviour of iterates of Mellin-Fejer type operators with respect to pointwise and uniform convergence. We introduce a new method in the construction of linear combinations of Mellin type operators using the iterated kernels. In some cases this provides a better order of approximation. 相似文献
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S. P. Eveson 《Integral Equations and Operator Theory》2008,62(4):585-589
We show that if V
α (α > 0) is the Riemann-Liouville fractional integration operator and T is an invertible operator on L
2(0, 1) which commutes with V , then TV
α is not supercyclic on L
2(0, 1); in particular, many Volterra convolution operators are not supercyclic. The technique is based on an argument used
by Gallardo-Gutiérrez and Montes-Rodríguez to show that V is not supercyclic. 相似文献