We obtain the complete characterization of those domains G ⊂ C which admit the so called estimate of the Cauchy integral, that is to say, ̨̨̨R ∂G f(z) dz ̨̨̨ ≤ C(G) ‖f‖∞ γ(E) for all E ⊂ G and f ∈ H∞(G \ E), where γ(E) is the analytic capacity of E. The corresponding result for continuous functions f and the continuous analytic capacity α(E) is also proved.

It is proved that a Banach space contains a subspace isomorphic to l(1) if (and only if) it has a bounded sequence with no weak-Cauchy subsequence. The proof yields that a sequence of subsets of a given set has a subsequence that is either convergent or Boolean independent.

The N-extended supersymmetric self-dual Poincaré supergravity equations provide a natural local description of supermanifolds possessing hyperkähler structure. These equations admit an economical formulation in chiral superspace. A reformulation in harmonic superspace encodes self-dual supervielbeins and superconnections in a graded skew-symmetric supermatrix superfield prepotential satisfying ...

We consider QED in a constant axial vector background. Lorentz invariance violation(LIV) occurs through radiative corrections. A detailed study of the phenomenology of the model is carried out, clarifying important issues related to the various regularizations employed . In this context, the physical meaning of the cutoffs induced by LIV is emphasized. Finally, finite temperature radiative corr...

In this work, we use Lorentz invariance violation (LIV) introduced as a generic modification to particle dispersion relations to study some consequences of single photon emission, known as vacuum Cherenkov radiation, and photon decay processes in cosmic and gamma rays. These processes are forbidden in a Lorentz invariant theory but allowed under the hypothesis of LIV. We show that the emission ...

Let D be the sheaf of analytic differential operators of n variables x1, . . . , xn. We consider a left ideal I of D generated by {l1, . . . , lm} which are in the Weyl algebra D = C〈x1, . . . , xn, ∂1, . . . , ∂n〉. If no confusion arises, we also denote by I the left ideal D ·{l1, . . . , ln} in D. Assume that D/I is holonomic. It was proved by M.Kashiwara that the germs of the k-th extension ...

We give elementary proofs of the theorems mentioned in the title. Our methods rely on a simple version of Ramsey theory and a martingale difference lemma. They also provide quantitative results: if a Banach space contains l only with a bad constant then every bounded sequence admits a subsequence which is “nearly” a weak Cauchy sequence.

In the framework of metric spaces, we introduce concept Geraghty-Ciric type contractions and show existence uniqueness fixed point such mappings. This result improves unifies those obtained by Geraghty (Proc. Amer. Math. Soc. 40, 604-608 (1973)) Ciric 45, 267-273, (1974)). Several technical lemmas are employed to ensure that a Picard sequence is Cauchy sequence. addition, two illustrative examp...