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1.
We consider an invertible operator on a Banach space whose spectrum is an interpolating set for Hölder classes. We show that if , , with and , then for all , assuming that satisfies suitable regularity conditions. When is a Hilbert space and (i.e. is a contraction), we show that under the same assumptions, is unitary and this is sharp.
2.
Petar S. Kenderov Warren B. Moors 《Proceedings of the American Mathematical Society》2006,134(5):1503-1512
In this paper we prove a theorem more general than the following. Suppose that is Lindelöf and -favourable and is Lindelöf and Cech-complete. Then for each separately continuous function there exists a residual set in such that is jointly continuous at each point of .
3.
Ph. Clé ment G. Gripenberg S-O. Londen 《Transactions of the American Mathematical Society》2000,352(5):2239-2260
The equation where and are fractional derivatives of order and is studied. It is shown that if , , and are Hölder-continuous and , then there is a solution such that and are Hölder-continuous as well. This is proved by first considering an abstract fractional evolution equation and then applying the results obtained to (). Finally the solution of () with is studied. 相似文献
4.
Cristian E. Gutié rrez David Hartenstine 《Transactions of the American Mathematical Society》2003,355(6):2477-2500
We study the properties of generalized solutions to the Monge-Ampère equation , where the Borel measure satisfies a condition, introduced by Jerison, that is weaker than the doubling property. When , this condition, which we call , admits the possibility of vanishing or becoming infinite. Our analysis extends the regularity theory (due to Caffarelli) available when , which implies that is doubling. The main difference between the case and the case when is bounded between two positive constants is the need to use a variant of the Aleksandrov maximum principle (due to Jerison) and some tools from convex geometry, in particular the Hausdorff metric.
5.
A class of triangular parabolic systems given on bounded domains of with arbitrary is investigated. Sufficient conditions on the structure of the systems are found to assure that weak solutions exist globally.
6.
We prove that a locally finite dimensional shift-invariant linear space of distributions must be a linear subspace of some shift-invariant space generated by finitely many compactly supported distributions. If the locally finite dimensional shift-invariant space is a subspace of the Hölder continuous space or the fractional Sobolev space , then the superspace can be chosen to be or , respectively.
7.
Yunguang Lu 《Proceedings of the American Mathematical Society》2002,130(5):1339-1343
This paper is concerned with the Hölder estimates of weak solutions of the Cauchy problem for the general degenerate parabolic equations
with the initial data , where the diffusion function can be a constant on a nonzero measure set, such as the equations of two-phase Stefan type. Some explicit Hölder exponents of the composition function with respect to the space variables are obtained by using the maximum principle.
with the initial data , where the diffusion function can be a constant on a nonzero measure set, such as the equations of two-phase Stefan type. Some explicit Hölder exponents of the composition function with respect to the space variables are obtained by using the maximum principle.
8.
Tonia Ricciardi 《Proceedings of the American Mathematical Society》2008,136(8):2771-2783
We obtain an estimate for the Hölder continuity exponent for weak solutions to the following elliptic equation in divergence form: where is a bounded open subset of and, for every , is a symmetric matrix with bounded measurable coefficients. Such an estimate ``interpolates' between the well-known estimate of Piccinini and Spagnolo in the isotropic case , where is a bounded measurable function, and our previous result in the unit determinant case . Furthermore, we show that our estimate is sharp. Indeed, for every we construct coefficient matrices such that is isotropic and has unit determinant, and such that our estimate for reduces to an equality, for every .
9.
V. Ya. Éiderman 《Mathematical Notes》1998,63(6):813-822
In the paper the connection between the Hausdorff measure
h
(E) of setsE and the analytic capacity(E), and also between
h
(E) and the capacity
+(E) generated by Cauchy potentials with nonnegative measures is studied. It is shown that if the integral 0t
–3
h
2(t)dt is divergent andh satisfies the regularity condition, then there exists a plane Cantor setE for which
h
(E)>0, but
+(E)=0. The proof is based on the estimate of
+(E
n
), whereE
n
is the set appearing at thenth step in the construction of a plane Cantor set.Translated fromMatematicheskie Zametki, Vol. 63, No. 6, pp. 923–934, June, 1998.I am grateful to M. S. Melnikov and X. Tolsa for information about the work [17] and for discussion of open problems.I wish to thank the Department of Mathematics of Uppsala University (Sweden) for the excellent conditions under which this research was begun, and to Professor M. Essén for the hospitality and support of this undertaking. I am grateful also to Professor P. Mattila and Professor S. Ya. Khavinson for very useful discussions of these problems.Research partially supported by the Royal Swedish Academy of Sciences, International Science Foundation (Grant MB 6000) and by Ministry of Education of Russia (Grant 95-0-1.7-52)This research was partially supported by the Royal Swedish Academy of Sciences, by the International Science Foundation under grant No. MB 6000 and by the Ministry of Education of Russia under grant No. 95-0-1.7-52. 相似文献
10.
Christine Laurent-Thié baut Mei-Chi Shaw 《Transactions of the American Mathematical Society》2005,357(1):151-177
We study the local solvability of the tangential Cauchy-Riemann equation on an open neighborhood of a point when is a generic -concave manifold of real codimension in , where . Our method is to first derive a homotopy formula for in when is the intersection of with a strongly pseudoconvex domain. The homotopy formula gives a local solution operator for any -closed form on without shrinking. We obtain Hölder and estimates up to the boundary for the solution operator. RÉSUMÉ. Nous étudions la résolubilité locale de l'opérateur de Cauchy- Riemann tangentiel sur un voisinage d'un point d'une sous-variété générique -concave de codimension quelconque de . Nous construisons une formule d'homotopie pour le sur , lorsque est l'intersection de et d'un domaine strictement pseudoconvexe. Nous obtenons ainsi un opérateur de résolution pour toute forme -fermée sur . Nous en déduisons des estimations et des estimations hölderiennes jusqu'au bord pour la solution de l'équation de Cauchy-Riemann tangentielle sur .
11.
丰德军等人在他们的相关的论文中介绍了齐次均匀康托集和偏齐次均匀康托集,在本文中我们构造介于两者之间的一类齐次Moran集,给出其豪斯多夫维数的精确计算公式,并讨论维数关于参数的不连续性. 相似文献
12.
13.
文研究了 N 指标 d 维广义α-stable过程自相交局部时增量的Holder律. 并利用所得自相交局部时的性质, 证明了该过程重点的存在性, 得到了该过程多重时的Hausdorff维数及测度的下界.所得结论包含并推广了广义布朗单及stable单相应的结果. 相似文献
14.
Boundedness of the Bergman type operators on mixed norm spaces 总被引:2,自引:0,他引:2
Yongmin Liu 《Proceedings of the American Mathematical Society》2002,130(8):2363-2367
Conditions sufficient for boundedness of the Bergman type operators on certain mixed norm spaces of functions on the unit ball of are given, and this is used to solve Gleason's problem for the mixed norm spaces .
15.
In this study, based on a new quantum integral identity, we establish some quantum estimates of Hermite-Hadamard type inequalities for convex functions. These results generalize and improve some known results given in literatures. 相似文献
16.
Ethan Akin Eli Glasner Benjamin Weiss 《Transactions of the American Mathematical Society》2008,360(7):3613-3630
We describe a self homeomorphism of the Cantor set and then show that its conjugacy class in the Polish group of all homeomorphisms of forms a dense subset of . We also provide an example of a locally compact, second countable topological group which has a dense conjugacy class.
17.
In this paper we provide a general method to prove that certain nonlinear families of continuous functions contain dense linear manifolds. An application is furnished.
18.
Yasuhiro Gotoh 《Proceedings of the American Mathematical Society》1999,127(5):1443-1451
Let denote the space of all positive superharmonic functions on a domain . Lindqvist showed that is a bounded subset of . Using this, we give a characterization of finitely connected -dimensional uniform domains and remarks on Hölder domains.
19.
Marí a C. Pereyra Lesley A. Ward 《Proceedings of the American Mathematical Society》1998,126(1):135-144
We analyze the stability of Muckenhoupt's and classes of weights under a nonlinear operation, the -operation. We prove that the dyadic doubling reverse Hölder classes are not preserved under the -operation, but the dyadic doubling classes are preserved for . We give an application to the structure of resolvent sets of dyadic paraproduct operators.
20.
Robert Rałowski 《Mathematical Logic Quarterly》2009,55(6):659-665
We show that under some conditions on a family A ? I there exists a subfamily A0 ? A such that ∪ A0 is nonmeasurable with respect to a fixed ideal I with Borel base of a fixed uncountable Polish space. Our result applies to the classical ideal of null subsets of the real line and to the ideal of first category subsets of the real line (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献