共查询到20条相似文献,搜索用时 46 毫秒
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Boris I. Golubov 《Analysis Mathematica》2006,32(3):173-205
Summary For the fractional dyadic derivative and integral, the following analogues of two theorems of Lebesgue are proved: the theorem
on differentiation of the indefinite Lebesgue integral of an integrable function at its Lebesgue points, and the theorem
on reconstruction of an absolutely continuous function by means of its derivative. Dyadic fractional analogues of the formula
of integration by parts are also obtained. In addition, some theorems are proved on dyadic fractional differentiation and
integration of a Lebesgue integral depending on a parameter. Most of the results are new even for dyadic derivatives and
integrals of natural order. 相似文献
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Ferenc Weisz 《Analysis Mathematica》1998,24(1):59-77
It is shown that the maximal operator of the one-dimensional dyadic derivative of the dyadic integral is bounded from the dyadic Hardy-Lorentz spaceH p,q toL p,q (1/2<p<∞, 0<q≤∞) and is of weak type (L 1,L 1). We define the twodimensional dyadic hybrid Hardy spaceH 1 ‖ and verify that the corresponding maximal operator of a two-dimensional function is of weak type (H 1 ‖ ,L 1). As a consequence, we obtain that the dyadic integral of a two-dimensional functionfεH 1 ‖ ?LlogL is dyadically differentiable and its derivative is a.e.f. 相似文献
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We prove a (sharp) pointwise estimate for positive dyadic shifts of complexity m which is linear in the complexity. This can be used to give a pointwise estimate for Calderón-Zygmund operators and to answer a question originally posed by Lerner. Several applications to weighted estimates for both multilinear Calderón-Zygmund operators and square functions are discussed. 相似文献
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In this paper we prove the two-dimensional pointwise differentiability (provided that the distance of the indices is bounded) of the integral of an integrable function on two-parameter bounded Vilenkin groups. 相似文献
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A.K. Lerner 《Journal of Mathematical Analysis and Applications》2004,289(1):248-259
In a recent paper (Studia Math. 138 (2000) 285-291) we proved pointwise estimates relating some classical maximal and singular integral operators. Here we show that, in a sense, there are more flexible inequalities which not only imply the previously known results but also give something new. In particular, they hold for the multilinear Calderón-Zygmund operators. This result gives a new approach to a recent work by Grafakos and Torres, and unifies some classical inequalities by Cotlar and Coifman and Fefferman. 相似文献
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Zhijian Qiu 《数学学报(英文版)》2009,25(7):1217-1222
Let G be an open subset in the extended complex plane and let A(G) denote the algebra of all functions analytic on G and continuous on G. We call a domain multi-nicely connected if there is a circular domain W and a conformal map ~ from W onto G such that the boundary value function of φ is univalent almost everywhere with respect to the arclength on aW. Suppose that every component of G is finitely connected and none of the components of G have single point boundary components. We show that for every bounded analytic function on G to be the pointwise limit of a bounded sequence of functions in A(G), it is necessary and sufficient that each component of G is multi-nicely connected and the harmonic measures of G are mutually singular. This generalizes the corresponding result of Davie for the case when the components of G are simply connected. 相似文献
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Andrei K. Lerner 《Proceedings of the American Mathematical Society》2003,131(5):1459-1469
In a recent paper we proved pointwise estimates relating some classical maximal and singular integral operators. Here we show that inequalities essentially of the same type hold for the Littlewood-Paley operators.
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, , , . , . ,
, x(0,1),x2–j
,j=1,2,..., 2
n
. , ka
k
0 k k. , (0, 1) , , , , . , . 相似文献
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On the pointwise maximum of convex functions 总被引:2,自引:0,他引:2
S. P. Fitzpatrick S. Simons 《Proceedings of the American Mathematical Society》2000,128(12):3553-3561
We study the conjugate of the maximum, , of and when and are proper convex lower semicontinuous functions on a Banach space . We show that on the bidual, , of provided that and satisfy the Attouch-Brézis constraint qualification, and we also derive formulae for and for the ``preconjugate' of .
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Jun Wang 《Journal of Mathematical Analysis and Applications》2011,379(2):637-812
Let K(a) be the symmetrical Cantor set generated by ?0(x)=ax and ?1(x)=ax+(1−a), where 0<a<1/2. Let s be the Hausdorff dimension of K(a) and μ the Cantor measure. In this paper, under the hypothesis that a is slightly greater than 1/3, we obtain the explicit formulas of the upper and lower s-densities Θ?s(μ,x), for every point x∈K(a). Moreover, we describe the range of a key quantity τ(x) in these formulas. 相似文献
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A linear algebra proof is given of the fact that the nullspace of a finite-rank linear projector, on polynomials in two complex variables, is an ideal if and only if the projector is the bounded pointwise limit of Lagrange projectors, i.e., projectors whose nullspace is a radical ideal, i.e., the set of all polynomials that vanish on a certain given finite set. A characterization of such projectors is also given in the real case. More generally, a characterization is given of those finite-rank linear projectors, on polynomials in d complex variables, with nullspace an ideal that are the bounded pointwise limit of Lagrange projectors. The characterization is in terms of a certain sequence of d commuting linear maps and so focuses attention on the algebra generated by such sequences. 相似文献
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For linear combinations of Gamma operators, if 0<a<2r, 1/2-1/2r≤λ≤l, or 0≤λ<1/2-1/2r(r≥2),0<a<r+10<a<(r+1)/1-λ, we obtain an equivalent theorem with ωuλρ(f ,t) instead of ωrλφ(f,t), where ωuφ(f,t) is theDitzian-Totik moduli of smoothness. 相似文献
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For linear combinations of Gamma operators, if 0 \frac12r \leqslant l\leqslant 1\frac{1}{2} - \frac{1}{{2r}} \leqslant \lambda \leqslant 1 , or 0 \leqslant l < \frac12 - \frac12r(r \geqslant 2)0 \leqslant \lambda< \frac{1}{2} - \frac{1}{{2r}}(r \geqslant 2) , 0 < a < \fracr + 11 - l0< a< \frac{{r + 1}}{{1 - \lambda }} , we obtain an equivalent theorem with 相似文献
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A. A. Korobov 《Journal of Applied and Industrial Mathematics》2011,5(2):231-239
We prove the pointwise completeness of the order n system with constant coefficients under the assumption that the matrices of the system split into square blocks of the same
size so that the collection of all blocks embeds into a finite dimensional associative division algebra; the block rank of
the passive matrix is at most 2. 相似文献
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For bounded or some locally bounded functions f measurable on an interval I there is estimated the rate of convergence of
the Durrmeyer-type operatorsL
f at those points xεIntI at which the one-sided limits f(x±0) exist. In the main theorems the Chanturiya's modulus of variation
is used. 相似文献
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Shmuel Friedland 《Israel Journal of Mathematics》1980,35(1-2):89-108
LetA(ε) andB(ε) be complex valued matrices analytic in ε at the origin.A(ε)≈
p
B(ε) ifA(ε) is similar toB(ε) for any |ε|<r,A(ε)≈a
B(ε) ifB(ε)=T(ε)A(ε)T
−1(ε) andT(ε) is analytic and |T(ε)|≠0 for |ε|<r! In this paper we find a necessary and sufficient conditions onA(ε) andB(ε) such thatA(ε)≈
a
B(ε) provided thatA(ε)≈
p
B(ε). This problem arises in study of certain ordinary differential equations singular with respect to a parameter ε in the
origin and was first stated by Wasow.
Sponsored by the United States Army under Contract No. DAAG29-75-C-0024 相似文献