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41.
We prove that a WLD subspace of the space consisting of all bounded, countably supported functions on a set Γ embeds isomorphically into if and only if it does not contain isometric copies of . Moreover, a subspace of is constructed that has an unconditional basis, does not embed into , and whose every weakly compact subset is separable (in particular, it cannot contain any isomorphic copies of ). 相似文献
42.
Sarika Goyal 《Mathematische Nachrichten》2019,292(10):2189-2202
In this article, we study the eigenvalues of p‐fractional Hardy operator where , , , and Ω is an unbounded domain in with Lipschitz boundary containing 0. The weight function V may change sign and may have singular points. We also show that the least positive eigenvalue is simple and it is uniquely associated to a nonnegative eigenfunction. Moreover, we proved that there exists a sequence of eigenvalues as . 相似文献
43.
We study “large” nonnegative solutions for a class of quasilinear equations model of which is We give a sufficient condition on the exponents and for the removability of isolated singularities. 相似文献
44.
Explicit and partly sharp estimates are given of integrals over the square of Bessel functions with an integrable weight which can be singular at the origin. They are uniform with respect to the order of the Bessel functions and provide explicit bounds for some smoothing estimates as well as for the L2 restrictions of Fourier transforms onto spheres in which are independent of the radius of the sphere. For more special weights these restrictions are shown to be Hölder continuous with a Hölder constant having this independence as well. To illustrate the use of these results a uniform resolvent estimate of the free Dirac operator with mass in dimensions is derived. 相似文献
45.
Steffen Lewitzka 《Annals of Pure and Applied Logic》2019,170(2):218-250
In previous work [15], we presented a hierarchy of classical modal systems, along with algebraic semantics, for the reasoning about intuitionistic truth, belief and knowledge. Deviating from Gödel's interpretation of IPC in S4, our modal systems contain IPC in the way established in [13]. The modal operator can be viewed as a predicate for intuitionistic truth, i.e. proof. Epistemic principles are partially adopted from Intuitionistic Epistemic Logic IEL [4]. In the present paper, we show that the S5-style systems of our hierarchy correspond to an extended Brouwer–Heyting–Kolmogorov interpretation and are complete w.r.t. a relational semantics based on intuitionistic general frames. In this sense, our S5-style logics are adequate and complete systems for the reasoning about proof combined with belief or knowledge. The proposed relational semantics is a uniform framework in which also IEL can be modeled. Verification-based intuitionistic knowledge formalized in IEL turns out to be a special case of the kind of knowledge described by our S5-style systems. 相似文献
46.
47.
A new capillary electrophoresis method was developed to study the synergistic effect of superoxide dismutase and jujuboside A or B on scavenging superoxide anion radical in serum matrix respectively, in which superoxide anion radical was generated from pyrogallol autoxidation. The electrophoresis conditions, and the factors affecting the productive rate of purpurogallin, such as pyrogallol autoxidation product and the activity of superoxide dismutase, were optimized. Under optimal conditions, the content of superoxide dismutase in Gibco newborn calf serum was 7.06 mg/L, RSD was 2.01% and the average recovery was 98.4%. The values of IC50 for jujuboside A and B in the serum matrix were 157.67 and 31.60 mg/L respectively, and they both had synergy on scavenging superoxide anion radical with superoxide dismutase, but there was no the dose‐dependency on this synergy. 相似文献
48.
The Adimurthi–Druet [1] inequality is an improvement of the standard Moser–Trudinger inequality by adding a -type perturbation, quantified by , where is the first Dirichlet eigenvalue of Δ on a smooth bounded domain. It is known [3], [10], [14], [19] that this inequality admits extremal functions, when the perturbation parameter α is small. By contrast, we prove here that the Adimurthi–Druet inequality does not admit any extremal, when the perturbation parameter α approaches . Our result is based on sharp expansions of the Dirichlet energy for blowing sequences of solutions of the corresponding Euler–Lagrange equation, which take into account the fact that the problem becomes singular as . 相似文献
49.
Xuan Thinh Duong Irina Holmes Ji Li Brett D. Wick Dongyong Yang 《Journal of Functional Analysis》2019,276(4):1007-1060
In this paper we establish the characterization of the weighted BMO via two weight commutators in the settings of the Neumann Laplacian on the upper half space and the reflection Neumann Laplacian on with respect to the weights associated to and respectively. This in turn yields a weak factorization for the corresponding weighted Hardy spaces, where in particular, the weighted class associated to is strictly larger than the Muckenhoupt weighted class and contains non-doubling weights. In our study, we also make contributions to the classical Muckenhoupt–Wheeden weighted Hardy space (BMO space respectively) by showing that it can be characterized via the area function (Carleson measure respectively) involving the semigroup generated by the Laplacian on and that the duality of these weighted Hardy and BMO spaces holds for Muckenhoupt weights with while the previously known related results cover only . We also point out that this two weight commutator theorem might not be true in the setting of general operators L, and in particular we show that it is not true when L is the Dirichlet Laplacian on . 相似文献
50.