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Weighted square function estimates
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abstract
The paper contains the proof of $L^p$-weighted norm inequalities for both, martingales square functions and the classical square functions in harmonic analysis of Littlewood-Paley and Lusin. Furthermore, the bounds are completely explicit and are optimal not only on the dependence of the characteristics of the weight but also on the dependance on $p$, as $p\to\infty$. The proof rests on Bellman function method: the estimates are deduced from the existence of an appropriate and rather complicated function of four variables.
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Cited by 1 Pith paper
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Korn's inequality from the viewpoint of calculus of variations
Korn's constant satisfies p^*-1 ≤ C(p,d) ≤ √3(p^*-1) in all dimensions, with exact p^*-1 for radial fields in dimension 2.
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