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1.
We apply the techniques of monotone and relative rearrangements to the nonrearrangement invariant spaces Lp()(Ω) with variable exponent. In particular, we show that the maps uLp()(Ω)→k(t)u*Lp*()(0,measΩ) and uLp()(Ω)→u*Lp*()(0,measΩ) are locally -Hölderian (u* (resp. p*) is the decreasing (resp. increasing) rearrangement of u (resp. p)). The pointwise relations for the relative rearrangement are applied to derive the Sobolev embedding with eventually discontinuous exponents. 相似文献
2.
Let M be a connected compact complex manifold endowed with a strongly pseudoconvex complex Finsler metric F. In this paper, we first define the complex horizontal Laplacian □h and complex vertical Laplacian □v on the holomorphic tangent bundle T1,0M of M, and then we obtain a precise relationship among □h,□v and the Hodge–Laplace operator on (T1,0M,,), where , is the induced Hermitian metric on T1,0M by F. As an application, we prove a vanishing theorem of holomorphic p-forms on M under the condition that F is a Kaehler Finsler metric on M. 相似文献
3.
It is first observed that a uniformly bounded cosine operator function C() and the associated sine function S() are totally non-stable. Then, using a zero-one law for the Abel limit of a closed linear operator, we prove some results concerning strong mean stability and uniform mean stability of C(). Among them are: (1) C() is strongly (C,1)-mean stable (or (C,2)-mean stable, or Abel-mean stable) if and only if 0ρ(A)σc(A); (2) C() is uniformly (C,2)-mean stable if and only if S() is uniformly (C,1)-mean stable, if and only if , if and only if , if and only if C() is uniformly Abel-mean stable, if and only if S() is uniformly Abel-mean stable, if and only if 0ρ(A). 相似文献
4.
The Monster group M contains a pair {C,N} of subgroups, where is the centralizer of an involution and N22+11+211.(M24×Sym3) is the normalizer of an elementary subgroup of order four with N∩C having index three in N. The amalgam {C,N} plays an important role in the existing constructions and uniqueness proofs for the Monster. We suggest a transparent construction of this amalgam. 相似文献
5.
Consider the multivariate linear model for the random matrixYn×pMN(XB, VΣ), whereBis the parameter matrix,Xis a model matrix, not necessarily of full rank, andVΣ is annp×nppositive-definite dispersion matrix. This paper presents sufficient conditions on the positive-definite matrixVsuch that the statistics for testingH0: CB=0vsHa: CB≠0have the same distribution as under the i.i.d. covariance structureIΣ. 相似文献
6.
Donglong Li Zhengde Dai Xuhong Liu 《Journal of Mathematical Analysis and Applications》2007,330(2):934-948
In this paper, the two-dimensional generalized complex Ginzburg–Landau equation (CGL)
ut=ρu−Δφ(u)−(1+iγ)Δu−νΔ2u−(1+iμ)|u|2σu+αλ1(|u|2u)+β(λ2)|u|2