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1.
Let be realhomogeneous functions in ofdegree and let bethe Borel measure on given by
where dx denotes theLebesgue measure on and > 0. Let T be the convolution operator and let
Assume that, for x 0, the followingtwo conditions hold: vanishes only at h = 0 and . In this paper we show that if then E is the empty set and if then E is the closed segment withendpoints and . Also, we give some examples.  相似文献   

2.
Let p (0, 1) be a real number and let n 2 be an even integer. We determine the largest value c n(p) such that the inequality
holds for all real numbers a 1,...,a n which are pairwise distinct and satisfy . Our theorem completes results of Ozeki, Mitrinovi-Kalajdi, and Russell, who found the optimal value c n(p) in the case p > 0 and n odd, and in the case p 1 and n even.  相似文献   

3.
In this paper we consider the existence and asymptotic behavior of solutions of the following problem:
where q>1, q1, >0, >0, 0, is the Laplacian in .  相似文献   

4.
We prove two versions of the Monotone Convergence Theorem for the vector integral of Kurzweil, , where R is a compact interval of , and f are functions with values on L(Z,W) and Z respectively, and Z and W are monotone ordered normed spaces. Analogous results can be obtained for the Kurzweil vector integral, , as well as to unbounded intervals R.  相似文献   

5.
Aliev  R. A. 《Mathematical Notes》2003,73(1-2):8-20
Suppose that is an arbitrary finite complex Borel measure on the interval is its Poisson integral, and are the conjugate harmonics of , and is the nontangential limiting value of the analytic function as . In this paper, we consider the problem of representing the analytic function in terms of its boundary values .  相似文献   

6.
In this paper the notions of uniformly upper and uniformly lower -estimates for Banach function spaces are introduced. Further, the pair (X, Y) of Banach function spaces is characterized, where X and Y satisfy uniformly a lower -estimate and uniformly an upper -estimate, respectively. The integral operator from X into Y of the form
is studied, where k, , are prescribed functions under some local integrability conditions, the kernel k is non-negative and is assumed to satisfy certain additional conditions, notably one of monotone type.  相似文献   

7.
Two results on composed functions are proven. First we give conditions on and so that the mean behaves like , if , including the examples
1$$ " align="middle" border="0"> , not an integer for . Secondly we find conditions on the real positive numbers , such that are almost periodic and we compute their mean values and spectra.  相似文献   

8.
The paper is concerned with oscillation properties of n-th order neutral differential equations of the form
0,$$ " align="middle" vspace="20%" border="0">
where c is a real number with with (t) < t and .Sufficient conditions are established for the existence of positive solutions and for oscillation of bounded solutions of the above equation. Combination of these conditions provides necessary and sufficient conditions for oscillation of bounded solutions of the equation. Furthermore, the results are generalized to equations in which c is a function of t and a certain type of a forcing term is present.  相似文献   

9.
A bi-Lipschitz continuous mapping of a space X is a bijection such that , where . We write if f is a Lipschitz (bi-Lipschitz) mapping of X into itself and denote by the set of all bi-Lipschitz mappings of X that are not isometry. Thus, if and blip . For X we consider a standard Cantor set K on the real line (with standard metric). The main result of this paper is formulated as follows: where Bibliography: 2 titles.  相似文献   

10.
A variety is called normal if no laws of the form s = t are valid in it where s is a variable and t is not a variable. Let L denote the lattice of all varieties of monounary algebras (A,f) and let V be a non-trivial non-normal element of L. Then V is of the form with some n > 0. It is shown that the smallest normal variety containing V is contained in for every m > 1 where C denotes the operator of forming choice algebras. Moreover, it is proved that the sublattice of L consisting of all normal elements of L is isomorphic to L.  相似文献   

11.
In this paper we investigate commutativity of rings with unity satisfying any one of the properties:
for some f(X) in and g(X), h(X) in where m 0, r 0, s 0, n > 0, t > 0 are non-negative integers. We also extend these results to the case when integral exponents in the underlying conditions are no longer fixed, rather they depend on the pair of ring elements x and y for their values. Further, under different appropriate constraints on commutators, commutativity of rings has been studied. These results generalize a number of commutativity theorems established recently.  相似文献   

12.
Let L(x, v) be a Lagrangian which is convex and superlinear in the velocity variable v, and let H(xp) be the associated Hamiltonian. Conditions are obtained under which every viscosity solution of the Hamilton-Jacobi equation
is an action function in the large, i.e.,
for all Received: 13 June 2003  相似文献   

13.
In this paper we prove two results. The first is an extension of the result of G. D. Jones [4[:Every nontrivial solution for
must be unbounded, provided , in and for every bounded subset I, f(t, z) is bounded in E × I.(B) Every bounded solution for , in , must be constant, provided in and for every bounded subset I, is bounded in .  相似文献   

14.
A differential calculus for random fields is developed and combined with the S-transform to obtain an explicit strong solution of the Cauchy problem
Here L is a linear second order elliptic operator, hi and c are real functions, and , where W t is a Brownian motion. An application of the solution to nonlinear filtering and mathematical finance is also considered.  相似文献   

15.
The paper deals with the problem of recovering the parameters (functions) and of the Maxwell dynamical system
(tan is the tangent component; is a solution) by the response operator ( is the normal). The parameters determine the velocity , the c-metric , and the time . It is shown that for any fixed , the operator determines and in uniquely. Bibliography: 15 titles.  相似文献   

16.
Qualitative comparison of the nonoscillatory behavior of the equations
and
is sought by way of finding different nonoscillation criteria for the above equations, L n is a disconjugate operator of the form
Both canonical and noncanonical forms of L n have been studied.  相似文献   

17.
Let C[-1,1] be the space of continuous functions f:[-1,1] with the uniform norm, let Pk be the Legendre polynomials such that Pk (1)=1, and let J0 be the Bessel function of zero index. We consider sequences of linear operators (summation methods) Un:C [-1,1] C[-1,1] defined by a multiplier function as follows:
The values , the norms of the operators Un , are called the Lebesgue constants of a summation method. The main result of this paper is the following statement. If a function is continuous on [\0,+),
is the FourierBessel transform of , and the function is summable on [\0,+) for some q>1, then
Bibliography: 8 titles.  相似文献   

18.
Let , and let be Epstein's zeta-function of the form Q. It is proved that for |t| > C > 0 one has the estimate
Bibliography: 9 titles.  相似文献   

19.
We obtain a strengthened version of the Kolmogorov comparison theorem. In particular, this enables us to obtain a strengthened Kolmogorov inequality for functions x L x (r), namely,
where
k, r N, k < r, and r is a perfect Euler spline of order r. Using this inequality, we strengthen the Bernstein inequality for trigonometric polynomials and the Tikhomirov inequality for splines. Some other applications of this inequality are also given.  相似文献   

20.
In this paper we establish the existence of nontrivial solutions to
with V x superlinear in x.  相似文献   

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