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- Svensson, Olof
(författare)
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Extensions of Fatou theorems in products of upper half-spaces
- 1995
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Ingår i: Mathematica Scandinavica. - Aarhus, Denmark : Aarhus Universitet, Mathematica Scandinavica. - 0025-5521 .- 1903-1807. ; 76:1, s. 139-151
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Tidskriftsartikel (refereegranskat)abstract
- We consider a multi-parameter maximal function and give a necessary and sufficient condition for its boundedness on Lp, P > 1. We also prove that the maximal function with suitable restriction parameters is of weak type (1,1).
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- Svensson, Olof
(författare)
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Nonadmissible convergence in symmetric spaces
- 1996
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Ingår i: Journal für die Reine und Angewandte Mathematik. - : Walter de Gruyter GmbH. - 0075-4102 .- 1435-5345. ; :472, s. 53-68
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Tidskriftsartikel (refereegranskat)abstract
- In the disc (or half-plane, or half-space) the well-known Fatou theorem says that the Poisson integral of an $L^1$-function has non-tangential boundary limits a.e. J. Marcinkiewicz and A. Zygmund cleared up the corresponding situation in products of discs (or half-spaces), introducing the notions of restricted and unrestricted non-tangential convergence. For general Riemannian symmetric spaces the corresponding notions ("restricted and unrestricted admissible convergence") have also been found, and the classical results generalized, some time ago. In 1984 A. Nagel and E. M. Stein investigated again the half-space case and found that the convergence theorem could be proved for slightly larger than nontangential approach domains (the exact description is too technical to state here). The subject of the present paper is to extend this investigation to general Riemannian symmetric spaces. The notion of restricted admissible convergence (which is the natural one for $L^1$-functions) is appropriately extended and the convergence theorem proved in a way which seems to be the final word on the subject. Unrestricted convergence (which goes with $L^p$ functions, $p>1$) is also discussed and a theorem proved, but only in the case of one particular example of a space of rank two. The proofs display considerable virtuosity in the application of real-variable methods.
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- Svensson, Olof, 1965
(författare)
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Time-Resolved and High-Energy Synchrotron Radiation Crystallography using X-ray Area Detectors: Calibration and Applications
- 1996
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis relates to characterisation and calibration techniques for X-ray area detectors with applications in time-resolved and high-energy X-ray crystallography. X-ray crystallography is an interdisciplinary science with important applications in many fields, e.g. chemistry, physics, biology, geology and materials science. With the advent of third generation synchrotron radiation (SR) sources, which offer X-ray beams of high flux, brilliance and energy, new areas of time-resolved crystallography (e.g. in-situ studies of phase transitions, chemical reactions and excited states) and high-energy crystallography (e.g. accurate structural studies) have become accessible. X-ray area detectors can simultaneously record a large solid angle of scattered X-ray photons. This is an important advantage, compared to point or one-dimensional detectors. However, X-ray area detectors are complicated, and can, due to various reasons (e.g. detector geometry), introduce distortions (i.e. systematic errors) into the acquired data. Given that these distortions are reproducible, they can be characterised and very largely corrected. In this thesis are developed techniques for characterisation and calibration of spatial distortion, non-uniformity of response and intensity non-linearity of X-ray area detectors, which were successfully used in a number of time-resolved and high-energy studies: Time-resolved in-situ study of the solid-state polymerisation of S2N2 to (SN)x using high-energy monochromatic X-ray powder diffraction. Apart from reaction kinetics, the experiment also yielded information relating to the polymerisation mechanism on both the macroscopic (bulk) and microscopic (atomic) level. Time-resolved study of the conversion of .alfa.-(ET)2I31 to .alfa.T-(ET)2I3 using high-energy monochromatic single-crystal diffraction: A metal-superconductor transition. The conversion was found to be of non-diffusive nature, and the structure of .alfa.T-(ET)2I3 was elucidated for the first time. Time-resolved single-crystal diffraction study of a phase transition in Ni3Sb. The transition was followed by recording the time evolution of individual peaks, and was found to be a diffusionless displacive transition. This thesis demonstrates the usefulness of the combination of X-ray area detectors and high-energy synchrotron radiation in general, and in particular the high data quality obtained after applying calibration techniques. 1 (where ET is bis(ethylenedithio)tetrathiafulvalene, C10S8H8)
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