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1.
In this paper, the authors first establish some new real-variable characterizations of Herz-type Hardy spaces
and
, where ω1,ω3 ∈ A1-weight, 1<q>∞,n(1−1/q)≤α<∞ and 0<p<∞. Then, using these new characterizations, they investigate the convergence of a bounded set in these spaces, and study
the boundedness of some potential operators on these spaces.
Supported by the NNSF of China 相似文献
2.
Jean-Christophe Bourgoin 《Calculus of Variations and Partial Differential Equations》2006,25(4):469-489
In this paper, we investigate the minimality of the map
from the Euclidean unit ball Bn to its boundary 핊n−1 for weighted energy functionals of the type Ep,f = ∫Bn f(r)‖∇ u‖p dx, where f is a non-negative function. We prove that in each of the two following cases:
Mathematics Subject Classification (2000) 58E20; 53C43 相似文献
i) | p = 1 and f is non-decreasing, |
ii) | p is integer, p ≤ n−1 and f = rα with α ≥ 0, the map minimizes Ep,f among the maps in W1,p(Bn, 핊n−1) which coincide with on ∂ Bn. We also study the case where f(r) = rα with −n+2 < α < 0 and prove that does not minimize Ep,f for α close to −n+2 and when n ≥ 6, for α close to 4−n. |
3.
We investigate Besov spaces and their connection with trigonometric polynomial approximation inL
p[−π,π], algebraic polynomial approximation inL
p[−1,1], algebraic polynomial approximation inL
p(S), and entire function of exponential type approximation inL
p(R), and characterizeK-functionals for certain pairs of function spaces including (L
p[−π,π],B
s
a(L
p[−π,π])), (L
p(R),s
a(Lp(R))),
, and
, where 0<s≤∞, 0<p<1,S is a simple polytope and 0<α<r.
This project is supported by the National Science Foundation of China. 相似文献
4.
K-functional, weighted moduli of smoothness, and best weighted polynomial approximation on a simplex
Song Li 《数学学报(英文版)》1999,15(3):395-406
An inverse theorem for the best weighted polynomial approximation of a function in
(S) is established. We also investigate Besov spaces generated by Freud weight and their connection with algebraic polynomial
approximation in
, wherew
α is a Jacobi-type weight onS, 0<p ≤ ∞,S is a simplex andW
λ is a Freud weight. For Ditzian-TotikK-functionals onL
p(S), 1 ≤p ≤ ∞, we obtain a new equivalence expression. 相似文献
5.
Manel Sanchón 《Potential Analysis》2007,27(3):217-224
We consider the equation on a smooth bounded domain of with zero Dirichlet boundary conditions where p ≥ 2, λ > 0 and f satisfies typical assumptions in the subject of extremal solutions. We prove that, for such general nonlinearities f, the extremal solution u
* belongs to L
∞ (Ω) if N < p + p/(p − 1) and if N < p(1 + p/(p − 1)).
This work was partially supported by MCyT BMF 2002-04613-CO3-02. 相似文献
6.
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.
相似文献
7.
In this paper, the boundedness of Toeplitz operator T
b(f) related to strongly singular Calderón-Zygmund operators and Lipschitz function b ε
(ℝn) is discussed from L
p(ℝn) to L
q(ℝn),
, and from L
p(ℝn) to Triebel-Lizorkin space
. We also obtain the boundedness of generalized Toeplitz operator Θ
α0
b
from L
p(ℝn) to L
q(ℝn),
. All the above results include the corresponding boundedness of commutators. Moreover, the boundedness of Toeplitz operator
T
b(f) related to strongly singular Calderón-Zygmund operators and BMO function b is discussed on L
p(ℝn), 1 < p < ∞. 相似文献
8.
We are studying the Diophantine exponent μ
n,l
defined for integers 1≤l<n and a vector α∈ℝ
n
by letting
where is the scalar product, denotes the distance to the nearest integer and is the generalised cone consisting of all vectors with the height attained among the first l coordinates. We show that the exponent takes all values in the interval [l+1,∞), with the value n attained for almost all α. We calculate the Hausdorff dimension of the set of vectors α with μ
n,l
(α)=μ for μ≥n. Finally, letting w
n
denote the exponent obtained by removing the restrictions on , we show that there are vectors α for which the gaps in the increasing sequence μ
n,1(α)≤...≤μ
n,n-1(α)≤w
n
(α) can be chosen to be arbitrary. 相似文献
9.
Abstract
In this paper, we establish the relationship between
Hausdorff measures and Bessel capacities on any nilpotent
stratified Lie group
(i. e., Carnot group). In particular, as a special corollary of
our much more general results, we have the following theorem
(see Theorems A and E in Section 1):
Let Q be the
homogeneous dimension of
.
Given any set E ⊂
,
B
α,p
(E) = 0 implies ℋ
Q−αp+ ε(E) = 0 for all ε > 0. On the other
hand, ℋ
Q−αp
(E) < ∞ implies
B
α,p
(E) = 0. Consequently, given any set
E ⊂
of Hausdorff dimension Q −
d, where 0 <
d <
Q, B
α,p
(E) = 0 holds if and only if αp ≤ d.
A version of O. Frostman’s theorem concerning Hausdorff
measures on any homogeneous space is also established using the
dyadic decomposition on such a space (see Theorem 4.4 in Section
4).
Research supported partly by the U. S. National
Science Foundation Grant No. DMS99–70352 相似文献
10.
J. Sunklodas 《Lithuanian Mathematical Journal》2005,45(4):475-486
We derive a lower bound of L
p
norms, 1 ⩽ p ⩽ ∞, in the central limit theorem for strongly mixing random variables X
1,..., X
n
with
under the boundedness condition ℙ{|X
i
| ⩽ M} = 1 with a nonrandom constantM > 0 and condition ∑
r⩾1
r
2α(r) < ∞, where α(r) are the Rosenblatt strong mixing coefficients.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 587–602, October–December, 2005. 相似文献
11.
For X
1 , X
2 , ..., X
n
a sequence of non-negative independent random variables with common distribution function F(t), X
(n) denotes the maximum and S
n
denotes the sum. The ratio variate R
n
= X
(n) / S
n
is a quantity arising in the analysis of process speedup and the performance of scheduling. O’Brien (J. Appl. Prob. 17:539–545,
1980) showed that as n → ∞, R
n
→0 almost surely iff is finite. Here we show that, provided either (1) is finite, or (2) 1 − F (t) is a regularly varying function with index ρ < − 1, then . An integral representation for the expected ratio is derived, and lower and upper asymptotic bounds are developed to obtain
the result. Since is often known or estimated asymptotically, this result quantifies the rate of convergence of the ratio’s expected value.
The result is applied to the performance of multiprocessor scheduling.
相似文献
12.
The central Campanato spaces and its application 总被引:2,自引:0,他引:2
Yang Dachun 《分析论及其应用》1994,10(4):85-99
Let 1<p<∞, α≥0 andK be a local field. In this paper, the author introduces the spaces J
p
α
(K) and the central Campanato spaces
as well as the Sp,α- and S
p,α
+
-type singular integrals. Then, the author investigates the behavior of these singular integrals and their altered operators
on these spaces.
The research was supported by the NNSF of China. 相似文献
13.
Dinh Dũng 《Advances in Computational Mathematics》2009,30(4):375-401
We investigate a problem of approximate non-linear sampling recovery of functions on the interval expressing the adaptive choice of n sampled values of a function to be recovered, and of n terms from a given family of functions Φ. More precisely, for each function f on , we choose a sequence of n points in , a sequence of n functions defined on and a sequence of n functions from a given family Φ. By this choice we define a (non-linear) sampling recovery method so that f is approximately recovered from the n sampled values f(ξ
1), f(ξ
2),..., f(ξ
n
), by the n-term linear combination
In searching an optimal sampling method, we study the quantity
where the infimum is taken over all sequences of n points, of n functions defined on , and of n functions from Φ. Let be the unit ball in the Besov space and M the set of centered B-spline wavelets
which do not vanish identically on , where N
r
is the B-spline of even order r = 2ρ ≥ [α] + 1 with knots at the points 0,1,...,r. For and α > 1, we proved the following asymptotic order
An asymptotically optimal non-linear sampling recovery method S
* for is constructed by using a quasi-interpolant wavelet representation of functions in the Besov space in terms of the B-splines
M
k,s
and the associated equivalent discrete quasi-norm of the Besov space. For 1 ≤ p < q ≤ ∞ , the asymptotic order of this asymptotically optimal sampling non-linear recovery method is better than the asymptotic
order of any linear sampling recovery method or, more generally, of any non-linear sampling recovery method of the form R(H,ξ,f): = H(f(ξ
1),...,f(ξ
n
)) with a fixed mapping and n fixed points
相似文献
14.
For 0 < α < mn and nonnegative integers n ≥ 2, m ≥ 1, the multilinear fractional integral is defined by
where = (y
1,y
2, ···, y
m
) and denotes the m-tuple (f
1,f
2, ···, f
m
). In this note, the one-weighted and two-weighted boundedness on L
p
(ℝ
n
) space for multilinear fractional integral operator I
α(m) and the fractional multi-sublinear maximal operator M
α(m) are established respectively. The authors also obtain two-weighted weak type estimate for the operator M
α(m).
Supported in Part by the NNSF of China under Grant #10771110, and by NSF of Ningbo City under Grant #2006A610090. 相似文献
15.
T. Shibata 《Annali di Matematica Pura ed Applicata》2007,186(3):525-537
We consider the nonlinear Sturm–Liouville problem
where λ > 0 is an eigenvalue parameter. To understand well the global behavior of the bifurcation branch in R
+ × L
2(I), we establish the precise asymptotic formula for λ(α), which is associated with eigenfunction u
α with ‖ u
α ‖2 = α, as α → ∞. It is shown that if for some constant p > 1 the function h(u) ≔ f(u)/u
p
satisfies adequate assumptions, including a slow growth at ∞, then λ(α) ∼ α
p−1
h(α) as α → ∞ and the second term of λ(α) as α → ∞ is determined by lim
u → ∞
uh′(u).
Mathematics Subject Classification (2000) 34B15 相似文献
(1) |
16.
Yu Cheng Li 《数学学报(英文版)》2008,24(10):1737-1750
In this paper, using the matrix skills and operator theory techniques we characterize the commutant of analytic Toeplitz operators on Bergman space. For f(z) = z^ng(z) (n ≥1), g(z) = b0 + b1z^p1 +b2z^p2 +.. , bk ≠ 0 (k = 0, 1, 2,...), our main result is =A′(Mf) = A′(Mzn)∩A′(Mg) = A′(Mz^s), where s = g.c.d.(n,p1,p2,...). In the last section, we study the relation between strongly irreducible curve and the winding number W(f,f(α)), α ∈ D. 相似文献
17.
If 0 < p < ∞ and α > − 1, the space
consists of those functions f which are analytic in the unit disc
and have the property that f ′ belongs to the weighted Bergman space Aαp. In 1999, Z. Wu obtained a characterization of the Carleson measures for the spaces
for certain values of p and α. In particular, he proved that, for 0 < p ≤ 2, the Carleson measures for the space
are precisely the classical Carleson measures. Wu also conjectured that this result remains true for 2 < p < ∞. In this paper we prove that this conjecture is false. Indeed, we prove that if 2 < p < ∞, then there exists g analytic in
such that the measure μg,p on
defined by dμg,p (z) = (1 − |z|2)p - 1| g ′ (z)|p dx dy is not a Carleson measure for
but is a classical Carleson measure. We obtain also some sufficient conditions for multipliers of the spaces
相似文献
18.
In this paper, it was proved that the commutator
generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from L
p1 (ℝ
n
) to L
p2 (ℝ
n
) if and only if b is a CṀO(ℝ
n
) function, where 1/p
1 − 1/p
2 = β/n, 1 < p
1 < ∞, 0 ⩽ β < n. Furthermore, the characterization of
on the homogenous Herz space
(ℝ
n
) was obtained.
This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 10571014, 10371080) and
the Doctoral Programme Foundation of Institute of Higher Education of China (Grant No. 20040027001) 相似文献
19.
For multiplicative functions ƒ(n), let the following conditions be satisfied: ƒ(n)≥0 ƒ(p
r)≤A
r,A>0, and for anyε>0 there exist constants
,α>0 such that
and Σ
p≤x
ƒ(p) lnp≥αx. For such functions, the following relation is proved:
. Hereτ(n) is the number of divisors ofn andC(ƒ) is a constant.
Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 443–456, September, 1998.
The work of the first author was supported by the Russian Foundation for Basic Research. 相似文献
20.
Manabu Naito 《Annali di Matematica Pura ed Applicata》2007,186(1):59-84
In this paper the even-order quasilinear ordinary differential equation
is considered under the hypotheses that n is even, D(α
i
)x = (|x|αi−1 x)′, α
i
> 0(i = 1,2,…, n), β > 0, and p(t) is a continuous, nonnegative, and eventually nontrivial function on an infinite interval [a, ∞), a > 0. The existence of positive solutions of (1.1) is discussed, and basic results to the classical equation
are extended to the more general equation (1.1). In particular, necessary and sufficient integral conditions for the existence
of positive solutions of (1.1) are established in the case α 1α2⋅s α
n
≠ β.
This research was partially supported by Grant-in-Aid for Scientific Research (No. 15340048), Japan Society for the Promotion
of Science.
Mathematics Subject Classification (2000) 34C10, 34C11 相似文献