In this paper we prove that for every infinite-dimensional Banach space X and every 1 p<+ there exists a strongly measurable X-valued p-Pettis integrable function on the unit circle T such that the X-valued harmonic function defined as its Poisson integral does not converge radially at any point of
On Generalizations of Fatou’s Theorem for the Integrals with General Kernels
✍ Scribed by Karagulyan, G. A.; Safaryan, M. H.
- Book ID
- 125379435
- Publisher
- Springer-Verlag
- Year
- 2014
- Tongue
- English
- Weight
- 230 KB
- Volume
- 25
- Category
- Article
- ISSN
- 1050-6926
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📜 SIMILAR VOLUMES
## Abstract Let $ T ^{A} \_{\Omega, \alpha} $ (0 < __α__ < __n__) be the generalized commutator generated by fractional integral with rough kernel and the __m__–th order remainder of the Taylor formula of a function A. In this paper, the (__L__^__p__^, __L__^__r__^) (__r__ > 1) boundedness, the wea
## Communicated by E. Meister In this article an existence. theorem is proved for the coagulation-fragmentation equation with unbounded kernelratesSolutionsareshown tobeinthespace.X+ = {ceL':S,"(l +x)lc(x)ldx < co} wheneverthe kernels satisfy certain growth propertics and the non-negative initial