共查询到20条相似文献,搜索用时 11 毫秒
1.
Prabir Burman 《Journal of Mathematical Analysis and Applications》2007,327(1):251-256
From the results of Dostanic [M.R. Dostanic, Asymptotic behavior of the singular values of fractional integral operators, J. Math. Anal. Appl. 175 (1993) 380-391] and V? and Gorenflo [Kim Tuan V?, R. Gorenflo, Singular values of fractional and Volterra integral operators, in: Inverse Problems and Applications to Geophysics, Industry, Medicine and Technology, Ho Chi Minh City, 1995, Ho Chi Minh City Math. Soc., Ho Chi Minh City, 1995, pp. 174-185] it is known that the jth singular value of the fractional integral operator of order α>0 is approximately (πj)−α for all large j. In this note we refine this result by obtaining sharp bounds for the singular values and use these bounds to show that the jth singular value is (πj)−α[1+O(j−1)]. 相似文献
2.
In the very influential paper [4] Caffarelli and Silvestre studied regularity of (?Δ)s, 0<s<1, by identifying fractional powers with a certain Dirichlet-to-Neumann operator. Stinga and Torrea [15] and Galé et al. [7] gave several more abstract versions of this extension procedure. The purpose of this paper is to study precise regularity properties of the Dirichlet and the Neumann problem in Hilbert spaces. Then the Dirichlet-to-Neumann operator becomes an isomorphism between interpolation spaces and its part in the underlying Hilbert space is exactly the fractional power. 相似文献
3.
A. Ashyralyev 《Journal of Mathematical Analysis and Applications》2009,357(1):232-236
Definitions of fractional derivatives and fractional powers of positive operators are considered. The connection of fractional derivatives with fractional powers of positive operators is presented. The formula for fractional difference derivative is obtained. 相似文献
4.
The present paper is in continuation to our recent paper [6] in these proceedings. Therein, three composition formulae for
a general class of fractional integral operators had been established. In this paper, we develop the Mellin transforms and
their inversions, the Mellin convolutions, the associated Parseval-Goldstein theorem and the images of the multivariableH-function together with applications for these operators. In all, seven theorems and two corollaries (involving the Konhauser
biorthogonal polynomials and the Jacobi polynomials) have been established in this paper. On account of the most general nature
of the polynomials S
n
m
[x] and the multivariableH-function whose product form the kernels of our operators, a large number of (new and known) interesting results involving
simpler polynomials and special functions (involving one or more variables) obtained by several authors and hitherto lying
scattered in the literature follow as special cases of our findings. We give here exact references to the results (in essence)
of seven research papers which follow as simple special cases of our theorems. 相似文献
5.
Area integral functions are introduced for sectorial operators on Lp-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on Lp spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on Hinfin functional calculus of sectorial operators on Lp-spaces hold true when the square functions are replaced by the area integral functions. 相似文献
6.
Saad Zagloul Rida 《Applicable analysis》2013,92(1-2):93-102
We derive none some explicit formula for the power of fractional order (differential and integral) operators. 相似文献
7.
We derive a probabilistic representation for the Fourier symbols of the generators of some stable processes. This short paper represents a bridge between probabilists and researchers working in PDE?s. 相似文献
8.
The present paper is devoted to the boundedness of fractional integral operators in Morrey spaces defined on quasimetric measure spaces. In particular, Sobolev, trace and weighted inequalities with power weights for potential operators are established. In the case when measure satisfies the doubling condition the derived conditions are simultaneously necessary and sufficient for appropriate inequalities. 相似文献
9.
《Mathematische Nachrichten》2017,290(17-18):2901-2908
We prove weighted estimates for fractional integral operators on central Morrey spaces. Our result covers the weighted theorem by De Napoli, Drelichman and Durán (2011). Our proof is different from theirs. 相似文献
10.
We prove sharp Lp−Lq endpoint bounds for singular fractional integral operators and related Fourier integral operators, under the nonvanishing rotational curvature hypothesis. 相似文献
11.
Weak estimates for commutators of fractional integral operators 总被引:4,自引:0,他引:4
By introducing a kind of maximal operator of the fractional order associated with the mean Luxemburg norm and using the technique
of the sharp function, the weak type LlogL estimates for the commutators of the fractional integral operator and the related
maximal operator are established. 相似文献
12.
We obtain the boundedness for the fractional integral operators from the modulation Hardy space μp,q to the modulation Hardy space μr,q for all 0 < p < ∞. The result is an extension of the known result for the case 1 < p < ∞ and it contains a larger range of r than those in the classical result of the Lp → Lr boundedness in the Lebesgue spaces. We also obtain some estimates on the modulation spaces for the bilinear fractional operators. 相似文献
13.
The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities. 相似文献
14.
Yasuo Komori‐Furuya 《Mathematische Nachrichten》2019,292(8):1751-1762
Moen (2016) proved weighted estimates for the bilinear fractional integrals where . We improve his results when and consider the case . As a corollary we obtain a bilinear Stein–Weiss inequality where . 相似文献
15.
Vagif S. Guliyev M.N. Omarova 《Journal of Mathematical Analysis and Applications》2008,340(2):1058-1068
Let be the Laguerre hypergroup which is the fundamental manifold of the radial function space for the Heisenberg group. In this paper we obtain necessary and sufficient conditions on the parameters for the boundedness of the fractional maximal operator and the fractional integral operator on the Laguerre hypergroup from the spaces to the spaces and from the spaces to the weak spaces . 相似文献
16.
Kwok-Pun Ho 《Integral Transforms and Special Functions》2017,28(11):801-812
The modular estimates for the fractional integral operators and the k-plane transforms are obtained in this paper. These estimates are obtained by using the modular estimates of Hardy operators and the modular interpolation theorem. 相似文献
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19.
Alexander Bendikov Patrick Maheux 《Transactions of the American Mathematical Society》2007,359(7):3085-3097
Assuming that a Nash type inequality is satisfied by a non-negative self-adjoint operator , we prove a Nash type inequality for the fractional powers of . Under some assumptions, we give ultracontractivity bounds for the semigroup generated by .
20.
R. Oinarov 《Siberian Mathematical Journal》2007,48(5):884-896
We introduce some nested classes of Volterra type integral operators. For the operators of these classes we establish criteria for boundedness and compactness in Lebesgue spaces. 相似文献