Browsing 1 - Oberwolfach Preprints (OWP) by MSC "42"
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Bochner-Riesz Means at the Critical Index: Weighted and Sparse Bounds
[OWP-2023-16] (Mathematisches Forschungsinstitut Oberwolfach, 2023-11-27)We consider Bochner-Riesz means on weighted $L^p$ spaces, at the critical index $\lambda(p)=d(\frac 1p-\frac 12)-\frac 12$. For every $A_1$-weight we obtain an extension of Vargas' weak type $(1,1)$ inequality in some range ... -
Coorbit Spaces and Dual Molecules: the Quasi-Banach Case
[OWP-2022-08] (Mathematisches Forschungsinstitut Oberwolfach, 2022-05-27)This paper provides a self-contained exposition of coorbit spaces associated with integrable group representations and quasi-Banach function spaces. It extends the theory in [Studia Math., 180(3):237–253, 2007] to locally ... -
Mehler-Heine asymptotics of a class of generalized hypergeometric polynomials :
[OWP-2013-23] (Mathematisches Forschungsinstitut Oberwolfach, 2013-10-29)We obtain a Mehler–Heine type formula for a class of generalized hypergeometric polynomials. This type of formula describes the asymptotics of polynomials scale conveniently. As a consequence of this formula, we obtain ... -
Multivariate Hybrid Orthogonal Functions
[OWP-2020-04] (Mathematisches Forschungsinstitut Oberwolfach, 2020-03-12)We consider multivariate orthogonal functions satisfying hybrid orthogonality conditions with respect to a moment functional. This kind of orthogonality means that the product of functions of different parity order ... -
A Note on Endpoint Bochner-Riesz Estimates
[OWP-2023-17] (Mathematisches Forschungsinstitut Oberwolfach, 2023-11-27)We revisit an $\varepsilon$-removal argument of Tao to obtain sharp $L^p \to L^r(L^p)$ estimates for sums of Bochner-Riesz bumps which are conditional on non-endpoint bounds for single scale bumps. These can be used to ... -
On Weak Weighted Estimates of Martingale Transform
[OWP-2016-22] (Mathematisches Forschungsinstitut Oberwolfach, 2016-11-12)We consider several weak type estimates for singular operators using the Bellman function approach. We disprove the $A_1$ conjecture, which stayed open after Muckenhoupt-Wheeden's conjecture was disproved by Reguera-Thiele. -
Weighted Fourier inequalities for radial functions
[OWP-2009-26] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-19)Weighted $L^p(\mathbb{R}^n) \to L^q(\mathbb{R}^n)$ Fourier inequalities are studied. We prove Pitt-Boas type results on integrability with power weights of the Fourier transform of a radial function.