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101.
J. Arvesú L. L. Littlejohn F. Marcellán 《Journal of Computational Analysis and Applications》2002,4(4):363-387
In this paper, we further develop the left-definite and right-definite spectral theory associated with the self-adjoint differential operator A in L2(-1,1), generated from the classical second-order Legendre differential equation, having the sequence of Legendre polynomials as eigenfunctions. Specifically, we determine the first three left-definite spaces associated with the pair (L2(-1,1),A). As a consequence of these results, we determine the explicit domain of both the associated left-definite operator A1, first observed by Everitt, and the self-adjoint operator A1/2. In addition, we give a new characterization of the domain D(A) of A and, as a corollary, we present a new proof of the Everitt-Mari result which gives optimal global smoothness of functions in D(A). 相似文献
102.
We obtain sufficient conditions for the continuity of the general nonlinear superposition operator (generalized Nemytskii operator) acting from the space
of differentiable functions on a bounded domain
to the Lebesgue space
. The values of operators on a function
are locally determined by the values of both the function
itself and all of its partial derivatives up to order
inclusive. In certain particular cases, the sufficient conditions obtained are proved to be necessary as well. The results are illustrated by several examples, and an application to the theory of Sobolev spaces is also given. 相似文献
103.
104.
It is known that shape preserving approximation has lower rates than unconstrained approximation. This is especially true for copositive and intertwining approximations. ForfLp, 1p<∞, the former only has rateω(f, n−1)p, and the latter cannot even be bounded byC fp. In this paper, we discuss various ways to relax the restrictions in these approximations and conclude that the most sensible way is the so-calledalmostcopositive/intertwining approximation in which one relaxes the restriction on the approximants in a neighborhood of radiusΔn(yj) of each sign changeyj. 相似文献
105.
This paper generalizes an inequality of Moser from the case that is in the Lebesgue space to certain subspaces, namely the Lorentz spaces , where . The conclusion is that is integrable, where . This is a higher degree of integrability than in the Moser inequality when . A formula for is given and it is also shown that no larger value of works.
106.
We prove the existence of a solution of the nonlinear equation in IRN and in exterior domains, respectively. We concentrate to the case when p ≥ N and the nonlinearity f(x, · ) is “superlinear” and “subcritical”. 相似文献
107.
Piotr Hajlasz 《Proceedings of the American Mathematical Society》1999,127(2):417-423
If is an open set with the sufficiently regular boundary, then the Hardy inequality holds for and , where . The main result of the paper is a pointwise inequality , where on the right hand side there is a kind of maximal function. The pointwise inequality combined with the Hardy-Littlewood maximal theorem implies the Hardy inequality. This generalizes some recent results of Lewis and Wannebo.
108.
The unique solvability of the airfoil (Prandtl) integro-differential equation on the semi-axis + = [0, ) is proved in the Sobolev space W
p
1
and Bessel potential spaces H
p
s
under certain restrictions on p and s. 相似文献
109.
Bernard Coupet Hervé Gaussier Alexandre Sukhov 《Proceedings of the American Mathematical Society》1999,127(11):3191-3200
We study rigidity and regularity properties of CR maps between smooth convex hypersurfaces of finite type in
110.
The aim of the paper is to develop the Fourier Analysis techniques needed in the study of optimal well-posedness and global regularity properties of the Yang-Mills equations in Minkowski space-time , for the case of the critical dimension . We introduce new functional spaces and prove new bilinear estimates for solutions of the homogeneous wave equation, which can be viewed as generalizations of the well-known Strichartz-Pecher inequalities.