共查询到20条相似文献,搜索用时 0 毫秒
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Teresa Martínez 《Mathematische Nachrichten》2003,251(1):52-63
For 1 < p < ∞, the almost surely finiteness of is a necessary and sufficient condition in order to have almost surely convergence of the sequences {E(f|?n)} with f ∈ Lp(v dP). This condition is also equivalent to have weighted inequalities from Lp(v dP) into Lp(u dP) for some weight u for Doob's maximal function, square function and generalized Burkholder martingale transforms. Similarly, E(u|?1) < ∞ turns out to be necessary and sufficient for the above weighted inequalities to hold for some v. 相似文献
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In this paper, we give a weighted form of the Hermite-Hadamard inequalities. Some applications of them are also derived. The results presented here would provide extensions of those given in earlier works. Finally we pose two interesting problems. 相似文献
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In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others
functional inequalities (weak Poincaré inequalities, general Beckner inequalities, etc.). We also discuss the quantitative
behaviour of relative entropy along a symmetric diffusion semi-group. In particular, we exhibit an example where Poincaré
inequality can not be used for deriving entropic convergence whence weak logarithmic Sobolev inequality ensures the result.
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Using isoperimetry and symmetrization we provide a unified framework to study the classical and logarithmic Sobolev inequalities. In particular, we obtain new Gaussian symmetrization inequalities and connect them with logarithmic Sobolev inequalities. Our methods are very general and can be easily adapted to more general contexts. 相似文献
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Combining rearrangement techniques with Gromov’s proof (via optimal mass transportation) of the 1-Sobolev inequality, we prove a sharp quantitative version of the anisotropic Sobolev inequality on BV(Rn). We also deduce, as a corollary of this result, a sharp stability estimate for the anisotropic 1-log-Sobolev inequality. 相似文献
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We prove well-posedness results for the initial value problem of the periodic KdV equation as well as Kam type results in classes of high regularity solutions. More precisely, we consider the problem in weighted Sobolev spaces, which comprise classical Sobolev spaces, Gevrey spaces, and analytic spaces. We show that the initial value problem is well posed in all spaces with subexponential decay of Fourier coefficients, and ‘almost well posed’ in spaces with exponential decay of Fourier coefficients. 相似文献
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Umberto Mosco 《Applicable analysis》2013,92(3):367-402
We present two-scale Morrey–Sobolev inequalities for measure-valued Lagrangeans on quasi-metric balls, scaled according to refined power laws. The fine tuning is given by suitable gauge functions, typically of logarithmic type. Fractal examples with fluctuating geometry are described. 相似文献
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Athanase Cotsiolis 《Journal of Mathematical Analysis and Applications》2004,295(1):225-236
We obtain sharp constants for Sobolev inequalities for higher order fractional derivatives. As an application, we give a new proof of a theorem of W. Beckner concerning conformally invariant higher-order differential operators on the sphere. 相似文献
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On weighted weak type inequalities for modified Hardy operators 总被引:3,自引:0,他引:3
F. J. Martí n-Reyes P. Ortega 《Proceedings of the American Mathematical Society》1998,126(6):1739-1746
We characterize the pairs of weights for which the modified Hardy operator applies into weak- where is a monotone function and .
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We compute the optimal constant for some weighted Poincaré inequalities obtained by Fausto Ferrari and Enrico Valdinoci in [F. Ferrari, E. Valdinoci, Some weighted Poincaré inequalities, Indiana Univ. Math. J. 58 (4) (2009) 1619-1637]. 相似文献
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In this paper we study the Gelfand and Kolmogorov numbers of Sobolev embeddings between weighted function spaces of Besov and Triebel–Lizorkin type with polynomial weights. The sharp asymptotic estimates are determined in the so-called non-limiting case. 相似文献
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Germán Fonseca 《Journal of Functional Analysis》2011,260(2):436-459
We study the initial value problem associated to the Benjamin-Ono equation. The aim is to establish persistence properties of the solution flow in the weighted Sobolev spaces , s∈R, s?1 and s?r. We also prove some unique continuation properties of the solution flow in these spaces. In particular, these continuation principles demonstrate that our persistence properties are sharp. 相似文献
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In order to extend the blow-up criterion of solutions to the Euler equations, Kozono and Taniuchi [H. Kozono, Y. Taniuchi, Limiting case of the Sobolev inequality in BMO, with application to the Euler equations, Comm. Math. Phys. 214 (2000) 191-200] have proved a logarithmic Sobolev inequality by means of isotropic (elliptic) BMO norm. In this paper, we show a parabolic version of the Kozono-Taniuchi inequality by means of anisotropic (parabolic) BMO norm. More precisely we give an upper bound for the L∞ norm of a function in terms of its parabolic BMO norm, up to a logarithmic correction involving its norm in some Sobolev space. As an application, we also explain how to apply this inequality in order to establish a long-time existence result for a class of nonlinear parabolic problems. 相似文献
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Filippo Gazzola Hans-Christoph Grunau 《NoDEA : Nonlinear Differential Equations and Applications》2001,8(1):35-44
Pucci and Serrin [21] conjecture that certain space dimensions behave 'critically' in a semilinear polyharmonic eigenvalue
problem. Up to now only a considerably weakened version of this conjecture could be shown. We prove that exactly in these
dimensions an embedding inequality for higher order Sobolev spaces on bounded domains with an optimal embedding constant may
be improved by adding a 'linear' remainder term, thereby giving further evidence to the conjecture of Pucci and Serrin from
a functional analytic point of view. Thanks to Brezis-Lieb [5] this result is already known for the space in dimension n=3; we extend it to the spaces (K>1) in the 'presumably' critical dimensions. Crucial tools are positivity results and a decomposition method with respect
to dual cones.
Received June 1999 相似文献
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Jumping nonlinearities and weighted Sobolev spaces 总被引:2,自引:0,他引:2
Working in a weighted Sobolev space, a new result involving jumping nonlinearities for a semilinear elliptic boundary value problem in a bounded domain in RN is established. The nonlinear part of the equation is assumed to grow at most linearly and to be at resonance with the first eigenvalue of the linear part on the right. On the left, the nonlinearity crosses over (or jumps over) several higher eigenvalues. Existence is obtained through the use of infinite-dimensional critical point theory in the context of weighted Sobolev spaces and appears to be new even for the standard Dirichlet problem for the Laplacian. 相似文献