Search Results: 1 - 10 of 100 matches for " "
All listed articles are free for downloading (OA Articles)
Page 1 /100
Display every page Item
Deviations of Riesz projections of Hill operators with singular potentials  [PDF]
Plamen Djakov,Boris Mityagin
Mathematics , 2008,
Abstract: It is shown that the deviations $P_n -P_n^0$ of Riesz projections $$ P_n = \frac{1}{2\pi i} \int_{C_n} (z-L)^{-1} dz, \quad C_n=\{|z-n^2|= n\}, $$ of Hill operators $L y = - y^{\prime \prime} + v(x) y, x \in [0,\pi],$ with zero and $H^{-1}$ periodic potentials go to zero as $n \to \infty $ even if we consider $P_n -P_n^0$ as operators from $L^1$ to $L^\infty. $ This implies that all $L^p$-norms are uniformly equivalent on the Riesz subspaces $Ran P_n. $
Large Deviations for Riesz Potentials of Additive Processes  [PDF]
R. Bass,X. Chen,J. Rosen
Mathematics , 2007,
Abstract: We study functionals of the form \[\zeta_{t}=\int_0^{t}...\int_0^{t} | X_1(s_1)+...+ X_p(s_p)|^{-\sigma}ds_1... ds_p\] where $X_1(t),..., X_p(t)$ are i.i.d. $d$-dimensional symmetric stable processes of index $0<\bb\le 2$. We obtain results about the large deviations and laws of the iterated logarithm for $\zeta_{t}$.
Riesz transform and Riesz potentials for Dunkl transform  [PDF]
Sundaram Thangavelu,Yuan Xu
Mathematics , 2004,
Abstract: Analogous of Riesz potentials and Riesz transforms are defined and studied for the Dunkl transform associated with a family of weighted functions that are invariant under a reflection group. The $L^p$ boundedness of these operators is established in certain cases.
Renormalization of potentials and generalized centers  [PDF]
Jun O'Hara
Mathematics , 2010, DOI: 10.1016/j.aam.2011.09.003
Abstract: We generalize the Riesz potential of a compact domain in $\mathbb{R}^{m}$ by introducing a renormalization of the $r^{\alpha-m}$-potential for $\alpha\le0$. This can be considered as generalization of the dual mixed volumes of convex bodies as introduced by Lutwak. We then study the points where the extreme values of the (renormalized) potentials are attained. These points can be considered as a generalization of the center of mass. We also show that only balls give extreme values among bodied with the same volume.
Reverse Triangle Inequalities for Riesz Potentials and Connections with Polarization  [PDF]
I. E. Pritsker,E. B. Saff,W. Wise
Mathematics , 2013,
Abstract: We study reverse triangle inequalities for Riesz potentials and their connection with polarization. This work generalizes inequalities for sup norms of products of polynomials, and reverse triangle inequalities for logarithmic potentials. The main tool used in the proofs is the representation for a power of the farthest distance function as a Riesz potential of a unit Borel measure.
On Isoperimetric Inequalities of Riesz Potentials and Applications  [PDF]
Tynysbek Sh. Kalmenov, Ernazar Nysanov, Bolys Sabitbek
Applied Mathematics (AM) , 2013, DOI: 10.4236/am.2013.47A001
Abstract: In this article, we prove certain isoperimetric inequalities for eigenvalues of Riesz potentials and show some applications of the results to a non-local boundary value problem of the Laplace operator.

An $L^1$-type estimate for Riesz potentials  [PDF]
Armin Schikorra,Daniel Spector,Jean Van Schaftingen
Mathematics , 2014,
Abstract: In this paper we establish new $L^1$-type estimates for the classical Riesz potentials of order $\alpha \in (0, N)$: \[ \|I_\alpha u\|_{L^{N/(N-\alpha)}(\mathbb{R}^N)} \leq C \|Ru\|_{L^1(\mathbb{R}^N;\mathbb{R}^N)}. \] This sharpens the result of Stein and Weiss on the mapping properties of Riesz potentials on the real Hardy space $\mathcal{H}^1(\mathbb{R}^N)$ and provides a new family of $L^1$-Sobolev inequalities for the Riesz fractional gradient.
Characterization of Riesz and Bessel potentials on variable Lebesgue spaces  [PDF]
Alexandre Almeida,Stefan Samko
Journal of Function Spaces and Applications , 2006, DOI: 10.1155/2006/610535
Abstract: Riesz and Bessel potential spaces are studied within the framework of the Lebesgue spaces with variable exponent. It is shown that the spaces of these potentials can be characterized in terms of convergence of hypersingular integrals, if one assumes that the exponent satisfies natural regularity conditions. As a consequence of this characterization, we describe a relation between the spaces of Riesz or Bessel potentials and the variable Sobolev spaces.
Some properties of the Riesz potentials in Dunkl analysis  [PDF]
Chokri Abdelkefi,Mongi Rachdi
Mathematics , 2013,
Abstract: In Dunkl theory on Rd which generalizes classical Fourier analysis, we study first the behavior at infinity of the Riesz potential of a non compactly supported function. Second, we give for 1
On the -Boundedness of Nonisotropic Spherical Riesz Potentials
Sarikaya MehmetZeki,Yildirim Hüseyin
Journal of Inequalities and Applications , 2007,
Abstract: We introduced the concept of nonisotropic spherical Riesz potential operators generated by the -distance of variable order on -sphere and its -boundedness were investigated.
Page 1 /100
Display every page Item

Copyright © 2008-2017 Open Access Library. All rights reserved.