共查询到20条相似文献,搜索用时 15 毫秒
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We prove that solutions for ¯ get 1/M-derivatives more than the data in Lp-Sobolev spaces on a bounded convex domain of finite type M by means of the integral kernel method. Also we prove that the Bergman projection is invariant under the Lp-Sobolev spaces of fractional orders by different methods from McNeal-Stein's. By using these results, we can get Lp-Sobolev estimates of order 1/M for the canonical solution for ¯.
The author was supported by grant No. R01-2000-000-00001-0 from the Basic Research Program of the Korea Science&Engineering Foundation. 相似文献
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Estela A. Gavosto 《Journal of Geometric Analysis》1997,7(4):593-609
We obtain Hölder estimates for the $\bar \partial - equation$ on some domains of finite type in ?n using proper mapping techniques. The domains considered are domains of finite type in the sense of D’Angelo and are defined by local coordinate expressions satisfying certain algebraic geometric conditions which prevent the existence of complex analytic varieties in the boundary of the domain. Using a proper mapping which is given by the finite type condition and which carries all the information about the intrinsic geometry of the boundary, we transform the finite type points into strongly pseudoconvex ones. At these strongly pseudoconvex points we compute an explicit solution using the Henkin integral formula and we obtain estimates that we are able to pull back to the original domain. We achieve this by exploiting the branching behavior of the proper mapping. We also construct some biholomorphic numerical invariants associated with some of the domains under consideration. 相似文献
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We prove Hölder type inequalities for integrals and conditional expectations involving the infinite product. Moreover, a generalized Doob maximal operator is introduced and weighted inequalities for this operator are established. 相似文献
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Gabor Toth 《Journal of Geometry》2013,104(3):585-598
In 2009 Schneider obtained stability estimates in terms of the Banach–Mazur distance for several geometric inequalities for convex bodies in an n-dimensional normed space ${\mathbb{E}^n}$ . A unique feature of his approach is to express fundamental geometric quantities in terms of a single function ${\rho:\mathfrak{B} \times \mathfrak{B} \to \mathbb{R}}$ defined on the family of all convex bodies ${\mathfrak{B}}$ in ${\mathbb{E}^n}$ . In this paper we show that (the logarithm of) the symmetrized ρ gives rise to a pseudo-metric d D on ${\mathfrak{B}}$ inducing, from our point of view, a finer topology than Banach–Mazur’s d BM . Further, d D induces a metric on the quotient ${\mathfrak{B}/{\rm Dil}^+}$ of ${\mathfrak{B}}$ by the relation of positive dilatation (homothety). Unlike its compact Banach–Mazur counterpart, d D is only “boundedly compact,” in particular, complete and locally compact. The general linear group ${{\rm GL}(\mathbb{E}^n)}$ acts on ${\mathfrak{B}/{\rm Dil}^+}$ by isometries with respect to d D , and the orbit space is naturally identified with the Banach–Mazur compactum ${\mathfrak{B}/{\rm Aff}}$ via the natural projection ${\pi:\mathfrak{B}/{\rm Dil}^+\to\mathfrak{B}/{\rm Aff}}$ , where Aff is the affine group of ${\mathbb{E}^n}$ . The metric d D has the advantage that many geometric quantities are explicitly computable. We show that d D provides a simpler and more fitting environment for the study of stability; in particular, all the estimates of Schneider turn out to be valid with d BM replaced by d D . 相似文献
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Guangyan Jia 《Archiv der Mathematik》2010,94(5):489-499
In this paper, we shall prove that for n > 1, the n-dimensional Jensen inequality holds for the g-expectation if and only if g is independent of y and linear with respect to z, in other words, the corresponding g-expectation must be linear. A Similar result also holds for the general nonlinear expectation defined in Coquet et al. (Prob. Theory Relat. Fields 123 (2002), 1–27 or Peng (Stochastic Methods in Finance Lectures, LNM 1856, 143–217, Springer-Verlag, Berlin, 2004). As an application of a special n-dimensional Jensen inequality for g-expectation, we give a sufficient condition for g under which the Hölder’s inequality and Minkowski’s inequality for the corresponding g-expectation hold true. 相似文献
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Tim Bedford 《Constructive Approximation》1989,5(1):33-48
We consider some self-affine fractal functions previously studied by Barnsleyet al. The graphs of these functions are invariant under certain affine scalings, and we extend their definition to allow the use of nonlinear scalings. The Hölder exponent,h, for these fractal functions is calculated and we show that there is a larger Hölder exponent,h
, defined at almost every point (with respect to Lebesgue measure). For a class of such functions defined using linear affinities these exponents are related to the box dimensionD
B of the graph byh2–D
Bh
.Communicated by Michael F. Barnsley. 相似文献
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B. F. Ivanov 《Vestnik St. Petersburg University: Mathematics》2017,50(4):354-363
Suppose that m ≥ 2, numbers p 1, …, p m ∈ (1, +∞] satisfy the inequality \(\frac{1}{{{p_1}}} + \cdots + \frac{1}{{{p_m}}} < 1\), and functions \({\gamma _1} \in {L^{{p_1}}}\left( {{?^1}} \right), \cdots ,{\gamma _m} \in {L^{{p_m}}}\left( {{?^1}} \right)\) are given. It is proved that if the set of “resonance” points of each of these functions is nonempty and the “nonresonance” condition holds (both notions were defined by the author for functions in L p (?1), p ∈ (1, +∞]), then \(\mathop {\sup }\limits_{a,b \in {R^1}} \left| {\mathop \smallint \limits_a^b \prod\limits_{k = 1}^m {[{\gamma _k}\left( \tau \right) + \Delta {\gamma _k}\left( \tau \right)]} d\tau } \right| \leqslant C\prod\limits_{k = 1}^m {{{\left\| {{\gamma _k} + \Delta {\gamma _k}} \right\|}_{L_{ak}^{pk}\left( {{R^1}} \right)}}} \) where the constant C > 0 is independent of the functions \(\Delta {\gamma _k} \in L_{ak}^{pk}\left( {{?^1}} \right)\) and \(L_{ak}^{pk}\left( {{?^1}} \right) \subset {L^{pk}}\left( {{?^1}} \right)\), 1 ≤ k ≤ m, are special normed spaces. A condition for the integral over ?1 of a product of functions to be bounded is also given. 相似文献
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Summary For second order linear elliptic problems, it is proved that theP
1-nonconforming finite element method has the sameL
-asymptotic accuracy as theP
1-conforming one. This result is applied to derive optimalL
-error estimates for both the displacement and the stress fields of the lowest order Raviart-Thomas mixed finite element method, and a superconvergence result at the barycenter of each element.Performed in the research program of Istituto di Analisi Numerica of C.N.R. of PaviaPartially supported by MPI, GNIM of CNR, ItalySupported by Consejo Nacional de Investigaciones Cientificas y Técnicas, Argentina 相似文献
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Some generalizations and refinements of the well-known Hölder’s inequality are obtained. 相似文献
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Let (X,≤) be a totally ordered set, T
X
the full transformation semigroup on X and E an arbitrary equivalence on X. We consider a subsemigroup of T
X
defined by
= T_X: x,y X,(x,y) Eandx y(x,y) Eandx y\mathit{EOP}_X=\{\alpha\in T_X:\forall x,y\in X,(x,y)\in E~\hbox{and}~x\leq y\Rightarrow(x\alpha,y\alpha)\in E~\hbox{and}~x\alpha\leq y\alpha\} 相似文献
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Alberto Seeger 《Positivity》2014,18(3):505-517
We prove the Lipschitz continuity of the maximal angle function on the set of closed convex cones in a Hilbert space. A similar result is obtained for the minimal angle function. On the other hand, we prove that the incenter of a solid cone and the circumcenter of a sharp cone behave in a locally Hölderian manner. 相似文献
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New better estimates, which are given in terms of elementary functions, for the function r → (2/π)(1 - r2)K(r)K (r) + log r appearing in Hübner's sharp upper bound for the Hersch-Pfluger distortion function are obtained. With these estimates, some known bounds for the Hersch-Pfluger distortion function in quasiconformal theory are improved, thus improving the explicit quasiconformal Schwarz lemma and some known estimates for the solutions to the Ramanujan modular equations. 相似文献
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Eric A. Carlen 《Archiv der Mathematik》2017,108(4):365-371
A labelled oriented graph (LOG) group is a group given by a presentation constructed in a certain way from a labelled oriented graph: examples include Wirtinger presentations of knot groups. We show how to obtain generators for the Schur Multiplier \(H_2(G)\) of a LOG group from the underlying LOG, and by exhibiting the n-string braid group \(B_n\) as a LOG group, we compute \(H_2(B_n)\). 相似文献
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