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991.
Pengtao Li 《Journal of Mathematical Analysis and Applications》2010,369(2):595-609
In this paper, we establish a link between Leray mollified solutions of the three-dimensional generalized Navier-Stokes equations and mild solutions for initial data in the adherence of the test functions for the norm of . This result applies to the usual incompressible Navier-Stokes equations. 相似文献
992.
Thomas Kühn Mieczys?aw Masty?o 《Journal of Mathematical Analysis and Applications》2010,369(1):408-1265
We estimate Weyl numbers and eigenvalues of operators via studying their abstract summing norms. In particular we prove estimates of these summing norms for abstract interpolation Lorentz spaces. For this we combine factorization theorems with estimates of concavity constants. Finally we apply our general eigenvalue results to integral operators with kernels of weakly singular type. We obtain asymptotically optimal estimates which extend the well-known classical results. 相似文献
993.
Lawrence A. Harris 《Journal of Mathematical Analysis and Applications》2010,368(1):374-381
Our object is to present an independent proof of the extension of V.A. Markov's theorem to Gâteaux derivatives of arbitrary order for continuous polynomials on any real normed linear space. The statement of this theorem differs little from the classical case for the real line except that absolute values are replaced by norms. Our proof depends only on elementary computations and explicit formulas and gives a new proof of the classical theorem as a special case. Our approach makes no use of the classical polynomial inequalities usually associated with Markov's theorem. Instead, the essential ingredients are a Lagrange interpolation formula for the Chebyshev nodes and a Christoffel-Darboux identity for the corresponding bivariate Lagrange polynomials. We use these tools to extend a single variable inequality of Rogosinski to the case of two real variables. The general Markov theorem is an easy consequence of this. 相似文献
994.
Carmen Fernández 《Advances in Mathematics》2010,224(5):1904-1926
We obtain a class of subsets of R2d such that the support of the short time Fourier transform (STFT) of a signal f∈L2(Rd) with respect to a window g∈L2(Rd) cannot belong to this class unless f or g is identically zero. Moreover we prove that the L2-norm of the STFT is essentially concentrated in the complement of such a set. A generalization to other Hilbert spaces of functions or distributions is also provided. To this aim we obtain some results on compactness of localization operators acting on weighted modulation Hilbert spaces. 相似文献
995.
Tsukasa Iwabuchi 《Journal of Differential Equations》2010,248(8):1972-2100
The Cauchy problems for Navier-Stokes equations and nonlinear heat equations are studied in modulation spaces . Though the case of the derivative index s=0 has been treated in our previous work, the case s≠0 is also treated in this paper. Our aim is to reveal the conditions of s, q and σ of for the existence of local and global solutions for initial data . 相似文献
996.
In this paper we prove an abstract version of Pietsch's domination theorem which unify a number of known Pietsch-type domination theorems for classes of mappings that generalize the ideal of absolutely p-summing linear operators. A final result shows that Pietsch-type dominations are totally free from algebraic conditions, such as linearity, multilinearity, etc. 相似文献
997.
E. Durand-Cartagena 《Journal of Mathematical Analysis and Applications》2010,363(2):525-548
For a metric space X, we study the space D∞(X) of bounded functions on X whose pointwise Lipschitz constant is uniformly bounded. D∞(X) is compared with the space LIP∞(X) of bounded Lipschitz functions on X, in terms of different properties regarding the geometry of X. We also obtain a Banach-Stone theorem in this context. In the case of a metric measure space, we also compare D∞(X) with the Newtonian-Sobolev space N1,∞(X). In particular, if X supports a doubling measure and satisfies a local Poincaré inequality, we obtain that D∞(X)=N1,∞(X). 相似文献
998.
In 1967 Komlós proved that for any sequence n{fn} in L1(μ), with ‖fn‖?M<∞ (where μ is a probability measure), there exists a subsequence n{gn} of n{fn} and a function g∈L1(μ) such that for any further subsequence n{hn} of n{gn},
999.
Árpad Bényi Diego Maldonado Andrea R. Nahmod Rodolfo H. Torres 《Mathematische Nachrichten》2010,283(9):1257-1276
Boundedness properties for bilinear paraproducts on several function spaces are presented. The methods are based on the realization of paraproducts as bilinear Calderón‐Zygmund operators and the molecular character‐ization of function spaces. This provides a unified approach for the study of paraproducts, recovering some know results and establishing several new (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
1000.