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R~n上加权弱Hardy空间中的Calderón-Zygmund型算子 总被引:1,自引:0,他引:1
作者引进了某些 Calderón-Zygmund型算子,并且讨论了它们在加权 Lebesgue空间、加权弱Lebesgue空间、加权Hardy空间和加权弱Hardy空间上的有界性.作者也考察了一些结果的尖锐性. 相似文献
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该文用Lebesgue-Stieltjes积分给出一个双曲型方程组广义解的新定义,在这个意义下证明了Cauchy问题整体广义解的存在性.这种解自然地包含了δ-激波. 相似文献
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该文用Lebesgue-Stieltjes积分给出一个双曲型方程组广义解的新定义,在这个意义下证明了Cauchy问题整体广义解的存在性。这种解自然地包含了δ-激波。 相似文献
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作者引进了某些 Calderón-Zygmund型算子,并且讨论了它们在加权 Lebesgue空间、加权弱Lebesgue空间、加权Hardy空间和加权弱Hardy空间上的有界性.作者也考察了一些结果的尖锐性. 相似文献
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Mcshane积分与可测函数许东福(集美师范专科学校)1958/57年,R·Henstock与J.Kurzweil分别给出一种Riemann完全型的积分[4],人们称为Henstock-Kurzweil积分(简记为H-积分)。它推广了Lebesgue... 相似文献
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本文借助于Lebesgue测度等工具研究了一类高阶非线性泛函微分方程解的渐近分类与振动性。 相似文献
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本文继续文[7]的工作,讨论序连续。有限广义Fuzzy测度的Lebesgue分解问题。 相似文献
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In this paper we compute the line integral of a complex function on a rectifiable cycle homologous to zero obtaining a Green’s
formula with multiplicities that involves the
of the function and the index of the cycle. We consider this formula in several settings and we obtain a sharp version in
terms of the Lebesgue integrability properties of the partial derivatives of the function. This result depends on the proven
fact that the index of a rectifiable cycle is square integrable with respect to the planar Lebesgue measure.
The work of both authors is partially supported by grants 2000SGR-00059, 2001SGR 00172 of Generalitat de Catalunya and BFM
2002-04072-C02-02 of Ministerio de Ciencia y Tecnologia 相似文献
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The Lebesgue decomposition theorem and the Radon–Nikodym theorem are the cornerstones of the classical measure theory. These theorems were generalized in several settings and several ways. Hassi, Sebestyén, and de Snoo recently proved a Lebesgue type decomposition theorem for nonnegative sesquilinear forms defined on complex linear spaces. The main purpose of this paper is to formulate and prove also a Radon–Nikodym type result in this setting. As an application, we present a Lebesgue type decomposition theorem and solve a special case of the infimum problem for densely defined (not necessarily bounded) positive operators. 相似文献
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Mikhlin’s ideas and results related to the theory of spaces L ρ p(·) with nonstandard growth are developed. These spaces are called Lebesgue spaces with variable index; they are used in mechanics, the theory of differential equations, and variational problems. The boundedness of Fourier multipliers and singular operators on the spaces L ρ p(·) are considered. All theorems are derived from an extrapolation theorem due to Rubio de Francia. The considerations essentially use theorems on the boundedness of operators and maximal Hardy-Littlewood functions on Lebesgue spaces with constant index. 相似文献
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We prove the weighted boundedness for a family of integral operators on Lebesgue spaces and local type spaces. To this end we show that can be controlled by the Calderón operator and a local maximal operator. This approach allows us to characterize the power weighted boundedness on Lebesgue spaces. 相似文献
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A nonnegative form on a complex linear space is decomposed with respect to another nonnegative form : it has a Lebesgue decomposition into an almost dominated form and a singular form. The part which is almost dominated is the largest form majorized by which is almost dominated by . The construction of the Lebesgue decomposition only involves notions from the complex linear space. An important ingredient in the construction is the new concept of the parallel sum of forms. By means of Hilbert space techniques the almost dominated and the singular parts are identified with the regular and a singular parts of the form. This decomposition addresses a problem posed by B. Simon. The Lebesgue decomposition of a pair of finite measures corresponds to the present decomposition of the forms which are induced by the measures. T. Ando's decomposition of a nonnegative bounded linear operator in a Hilbert space with respect to another nonnegative bounded linear operator is a consequence. It is shown that the decomposition of positive definite kernels involving families of forms also belongs to the present context. The Lebesgue decomposition is an example of a Lebesgue type decomposition, i.e., any decomposition into an almost dominated and a singular part. There is a necessary and sufficient condition for a Lebesgue type decomposition to be unique. This condition is inspired by the work of Ando concerning uniqueness questions. 相似文献
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V.M. Kokilashvili 《Journal of Mathematical Analysis and Applications》2009,352(1):15-34
Last years there was increasing an interest to the so-called function spaces with non-standard growth, known also as variable exponent Lebesgue spaces. For weighted such spaces on homogeneous spaces, we develop a certain variant of Rubio de Francia's extrapolation theorem. This extrapolation theorem is applied to obtain the boundedness in such spaces of various operators of harmonic analysis, such as maximal and singular operators, potential operators, Fourier multipliers, dominants of partial sums of trigonometric Fourier series and others, in weighted Lebesgue spaces with variable exponent. There are also given their vector-valued analogues. 相似文献
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We compute the right and left democracy functions of admissible wavelet bases in variable Lebesgue spaces defined on \(\mathbb R^n\). As an application we give Lebesgue type inequalities for these wavelet bases. We also show that our techniques can be easily modified to prove analogous results for weighted variable Lebesgue spaces and variable exponent Triebel–Lizorkin spaces. 相似文献
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We consider subsets of Lebesgue spaces which are defined by pointwise constraints. We provide formulas for corresponding variational objects (tangent and normal cones). Our main result shows that the limiting normal cone is always dense in the Clarke normal cone and contains the convex hull of the pointwise limiting normal cone. A crucial assumption for this result is that the underlying measure is non-atomic, and this is satisfied in many important applications (Lebesgue measure on subsets of \(\mathbb {R}^{d}\) or the surface measure on hypersurfaces in \(\mathbb {R}^{d}\)). Finally, we apply our findings to an optimization problem with complementarity constraints in Lebesgue spaces. 相似文献
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Emmanuel Giner 《Set-Valued and Variational Analysis》2007,15(2):125-138
We give complete characterizations of integral functionals which are Lipschitzian on a Lebesgue space L p with p ≠ ∞. When the measure is atomless, we characterize the integral functionals which are locally Lipschitzian on such Lebesgue spaces. In every cases, the Lipchitzian properties of the integral functional can be described by growth conditions on the subdifferentials of the integrand which are equivalent to Lipschitzian properties of the integrand. 相似文献
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Rafael Serrano 《Archiv der Mathematik》2013,101(3):253-257
Using a generalized version of the Weyl–Riesz criterion for compactness of subsets of Lebesgue–Bochner spaces, we present in this short note an alternative proof of a result by J. Simon [4] that extends the classical result by J.P. Aubin and J.L. Lions on compact embeddings in Lebesgue–Bochner spaces to the non-reflexive Banach space case. 相似文献