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1.
In this paper we establish results on the existence of nontangential limits for weighted
-harmonic functions in the weighted Sobolev space
, for some q>1 and w in the Muckenhoupt A
q
class, where
is the unit ball in
. These results generalize the ones in Sect. 3 of Koskela et al., Trans. Am. Math. Soc. 348(2), 755–766, 1996, where the weight was identically equal to one. Weighted
-harmonic functions are weak solutions of the partial differential equation
where
for some fixed q∈(1,∞), where 0<α≤β<∞, and w(x) is a q-admissible weight as in Chap. 1 of Heinonen et al., Nonlinear Potential Theory, 2006.
Later, we apply these results to improve on results of Koskela et al., Trans. Am. Math. Soc. 348(2), 755–766, 1996 and Martio and Srebro, Math. Scand. 85, 49–70, 1999 on the existence of radial limits for bounded quasiregular mappings in the unit ball of
with some growth restriction on their multiplicity function.
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2.
In this paper, we prove two main results. The first one is to give a new condition for the existence of two-parameter -variation path integrals. Our condition of locally bounded -variation is more natural and easy to verify than those of Young. This result can be easily generalized to multi-parameter case. The second result is to define the integral of local time pathwise and then give generalized It’s formula when is only of bounded -variation in . In the case that is of locally bounded variation in , the integral is the Lebesgue–Stieltjes integral and was used by Elworthy, Truman and Zhao. When is of only locally -variation, where , , and , the integral is a two-parameter Young integral of -variation rather than a Lebesgue–Stieltjes integral. In the special case that is independent of , we give a new condition for Meyer's formula and is defined pathwise as a Young integral. For this we prove the local time is of -variation in for each , for each almost surely (-variation in the sense of Lyons and Young, i.e. ). 相似文献
3.
Aleksi Vähäkangas 《Potential Analysis》2007,27(1):27-44
We study the Dirichlet problem at infinity for -harmonic functions on a Cartan–Hadamard manifold M and give a sufficient condition for a point at infinity x
0∈M(∞) to be -regular. This condition is local in the sense that it only involves sectional curvatures of M in a set U∩M, where U is an arbitrary neighborhood of x
0 in the cone topology. The results apply to the Laplacian and p-Laplacian, 1<p<∞, as special cases.
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4.
With every subset selection for posets, there is associated a certain ideal completion . As shown by Erné, such completions help to extend classical results on domains and similar structures in the absence of
the required joins. Some results about –predistributive or –precontinuous posets and –continuous functions are summarized and supplemented. In particular, several central results on function spaces in domain
theory are extended to the setting of productive closed subset selections. The category FSBP, in which objects are finitely separated and upper bounded posets and arrows are continuous functions between them, is shown to be cartesian closed.
This research is supported by the National Natural Science Foundation of China, 10471035. 相似文献
5.
A new necessary and sufficient condition for the row
-property is given. By using this new condition and a special row rearrangement, we provide two global error bounds for the
extended vertical linear complementarity problem under the row
-property, which extend the error bounds given in Chen and Xiang (Math. Program. 106:513–525, 2006) and Mathias and Pang (Linear Algebra Appl. 132:123–136, 1990) for the P-matrix linear complementarity problem, respectively. We show that one of the new error bounds is sharper than
the other, and it can be computed easily for some special class of the row
-property block matrix. Numerical examples are given to illustrate the error bounds.
The work was in part supported by a Grant-in-Aid from Japan Society for the Promotion of Science, and the National Natural
Science Foundation of China (10671010). 相似文献
6.
The aim of this paper is to give some representation formulas of Riesz and Poisson-Jensen type for super-solutions to a class
of hypoelliptic ultraparabolic operators on a homogeneous Lie group . Our results complete the ones obtained in Cinti (Math Scand 100:1–21, 2007). We also provide a suitable theory for -Green functions and for -Green potentials of Radon measures. The proofs mostly rely on the use of appropriate techniques relevant to the Potential
Theory for .
Investigation supported by University of Bologna. Funds for selected research topics. 相似文献
7.
E. Ekici 《Acta Mathematica Hungarica》2007,117(4):325-333
The main purpose of this paper is to introduce the concepts of *-sets, *-continuous functions and to obtain new decompositions of continuous and ηζ-continuous functions. Moreover, properties of *-sets and some properties of -sets are discussed.
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8.
From light tails to heavy tails through multiplier 总被引:1,自引:1,他引:0
Qihe Tang 《Extremes》2008,11(4):379-391
Let X and Y be two independent nonnegative random variables, of which X has a distribution belonging to the class or for some γ ≥ 0 and Y is unbounded. We study how their product XY inherits the tail behavior of X. Under some mild technical assumptions we prove that the distribution of XY belongs to the class or accordingly. Hence, the multiplier Y builds a bridge between light tails and heavy tails.
相似文献
9.
Hany M. El-Hosseiny 《Potential Analysis》2006,25(2):131-145
We prove general boundary limit theorems of abelian type for quotients of functions defined in the half space . The functions considered are defined as convolutions of a kernel with Borel measures defined on the boundary . Our theorems are of the form
where the approach to the limit in question is either non-tangential (Theorems 3.4 and 3.3), or radial (Theorem 3.2). The key feature is the relation of subordination in the sense of Bochner between the two kernels and . Our results generalize many known ones, such as the abelian theorem of Doob and that of Armitage for relative harmonic functions, and the results of Watson and Doob for Parabolic functions. 相似文献
10.
Existence and Stability Results for Renormalized Solutions to Noncoercive Nonlinear Elliptic Equations with Measure Data 总被引:1,自引:0,他引:1
In this paper we prove the existence of a renormalized solution to a class of nonlinear elliptic problems whose prototype is
where is a bounded open subset of , , is the so-called Laplace operator, , is a Radon measure with bounded variation on , , , and belong to the Lorentz spaces , and , respectively. In particular we prove the existence result under the assumption that , is small enough and , with . We also prove a stability result for renormalized solutions to a class of noncoercive equations whose prototype is with . 相似文献
11.
In the study of the asymptotic behaviour of solutions of differential-difference equations the
-spectrum has been useful, where
and
implies Fourier transform
, with
given
, φ∈L
∞(ℝ,X), X a Banach space,
(half)line. Here we study
and related concepts, give relations between them, especially
weak Laplace half-line spectrum of φ, and thus ⊂ classical Beurling spectrum = Carleman spectrum =
; also
= Beurling spectrum of “φ modulo
” (Chill-Fasangova). If
satisfies a Loomis type condition (L
U
), then
countable and
uniformly continuous ∈U are shown to imply
; here (L
U
) usually means
, indefinite integral Pf of f in U imply Pf in
(the Bohl-Bohr theorem for
= almost periodic functions, U=bounded functions). This spectral characterization and other results are extended to unbounded functions via mean classes
, ℳ
m
U ((2.1) below) and even to distributions, generalizing various recent results for uniformly continuous bounded φ. Furthermore for solutions of convolution systems S*φ=b with
in some
we show
. With these above results, one gets generalizations of earlier results on the asymptotic behaviour of solutions of neutral
integro-differential-difference systems. Also many examples and special cases are discussed. 相似文献
12.
Andrzej Komisarski 《Journal of Theoretical Probability》2008,21(4):812-823
For a probability space (Ω,ℱ,P) and two sub-σ-fields
we consider two natural distances:
and
. We investigate basic properties of these distances. In particular we show that if a distance (ρ or
) from ℬ to
is small then there exists Z∈ℱ with small P(Z), such that for every B∈ℬ there exists
such that B∖Z and A∖Z differ by a set of probability zero. This improves results of Neveu (Ann. Math. Stat. 43(4):1369–1371, [1972]), Jajte and Paszkiewicz (Probab. Math. Stat. 19(1):181–201, [1999]).
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13.
Let be a convex function and be its Legendre tranform. It is proved that if is invariant by changes of signs, then . This is a functional version of the inverse Santaló inequality for unconditional convex bodies due to J. Saint Raymond.
The proof involves a general result on increasing functions on together with a functional form of Lozanovskii’s lemma. In the last section, we prove that for some c > 0, one has always . This generalizes a result of B. Klartag and V. Milman.
相似文献
14.
Given two vectors x, y in a Hilbert space and a weakly closed -module , we provide a necessary and sufficient condition for the existence of a compact operator T in satisfying Tx = y. 相似文献
15.
We prove the meromorphic version of the Weil–Oka approximation theorem in a reduced Stein space X and give some characterizations of meromorphically
-convex open sets of X. As an application we prove that for every meromorphically
-convex open set D of a reduced Stein space X with no isolated points there exists a family
of holomorphic functions on X such that the normality domain
of
coincides with D. Mathematics Subject Classification (2000) 32E10, 32C15, 32E30, 32A19 相似文献
16.
Linus Carlsson 《Mathematische Zeitschrift》2009,261(1):189-200
We show a sufficient condition for a domain in to be a H
∞-domain of holomorphy. Furthermore if a domain has the Gleason property at a point and the projection of the n − 1th order generalized Shilov boundary does not coincide with Ω then is schlicht. We also give two examples of pseudoconvex domains in which the spectrum is non-schlicht and satisfy several
other interesting properties.
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17.
Martin Kassabov 《Inventiones Mathematicae》2007,170(2):327-354
We construct explicit generating sets S
n
and of the alternating and the symmetric groups, which turn the Cayley graphs and into a family of bounded degree expanders for all n. 相似文献
18.
Given an open set in , we prove that every function in is zero everywhere on the boundary if and only if is regular in capacity. If in addition is bounded, then it is regular in capacity if and only if the mapping from into is injective, where denotes the Perron solution of the Dirichlet problem. Let be the set of all open subsets of which are regular in capacity. Then one can define metrics and on only involving the resolvent of the Dirichlet Laplacian. Convergence in those metrics will be defined to be the local/global uniform convergence of the resolvent of the Dirichlet Laplacian applied to the constant function . We prove that the spaces and are complete and contain the set of all open sets which are regular in the sense of Wiener (or Dirichlet regular) as a closed subset. 相似文献
19.
Ameer Athavale 《Complex Analysis and Operator Theory》2008,2(3):417-428
Let be a strictly pseudoconvex bounded domain in with C
2 boundary . If a subnormal m-tuple T of Hilbert space operators has the spectral measure of its minimal normal extension N supported on , then T is referred to as a -isometry. Using some non-trivial approximation theorems in the theory of several complex variables, we establish a commutant
lifting theorem for those -isometries whose (joint) Taylor spectra are contained in a special superdomain Ω of . Further, we provide a function-theoretic characterization of those subnormal tuples whose Taylor spectra are contained in
Ω and that are quasisimilar to a certain (fixed) -isometry T (of which the multiplication tuple on the Hardy space of the unit ball in is a rather special example).
Submitted: September 9, 2007. Revised: October 10, 2007. Accepted: October 24, 2007. 相似文献
20.
A. Krajka 《Acta Appl Math》2007,96(1-3):327-338
Let
be a probability space with a nonatomic measure P and let (S,ρ) be a separable complete metric space. Let {N
n
,n≥1} be an arbitrary sequence of positive-integer valued random variables. Let {F
k
,k≥1} be a family of probability laws and let X be some random element defined on
and taking values in (S,ρ).
In this paper we present necessary and sufficient conditions under which one can construct an array of random elements {X
n,k
,n,k≥1} defined on the same probability space and taking values in (S,ρ), and such that
, and moreover
as n→∞. Furthermore, we consider the speed of convergence
to X as n→∞.
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