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71.
In this note a representation of the discrete Green's function of a compact discretization of a two point boundary value problem of order n 2 is given which among other things allows a direct proff of the convergence (and divergence) properties. 相似文献
72.
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
73.
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
74.
Joachim Toft 《Applied and Computational Harmonic Analysis》2019,46(1):154-176
We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.We use these results to prove that the pseudo-differential operator is a Schatten-q operator from to and r-nuclear operator from to when for suitable p, q and r in . 相似文献
75.
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
76.
77.
For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function on the upper half‐spaces. Using the decomposition, we study the boundedness of . We obtain a natural extension to the multilinear setting of Muckenhoupt's weak‐type characterization. We also partially obtain characterizations of Muckenhoupt's strong‐type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates. 相似文献
78.
79.
《偏微分方程通讯》2013,38(11-12):2513-2525
ABSTRACT The Hopf map from minimal surfaces in H 3 to holomorphic quadratic differentials on H 2 is considered. Whether or not a given quadratic differential is in the image of this map is determined by the global existence/non-existence of solutions to a certain quasi-linear PDE. It is shown that this map is not surjective. 相似文献
80.
In a route towards enantiomerically enriched 1-(β-hydroxypropyl)indoles, which are potentially useful building blocks for high value-added chemicals synthesis, a kinetic resolution approach by means of lipase-catalyzed enantioselective acylation as well as hydrolysis/methanolysis has been elaborated for the first time. The enzymatic resolution of chiral N-substituted indole-based sec-alcohols was successfully accomplished, yielding both enantiomeric forms of the employed derivatives with up to >99% enantiomeric purity via an enantioselective transesterification under mild reaction conditions. The most selective resolutions were obtained using fungal (CAL-B and TLL) and bacterial (PFL and BCL) lipases and vinyl acetate as the acyl?group donor. The synthetic protocol described herein is very simple, user-friendly and efficient, thus paving the way for future access towards more complex compounds of this type. The absolute configurations of novel enantiomeric derivatives, and thus stereoselectivity of the described enzymatic reactions were confirmed by application of CDA-based NMR methodology and single-crystal X-ray diffraction analysis. 相似文献