Weak-type (1,1) estimates for strongly singular operators

DOI10.1007/S10476-019-0925-XzbMATH Open1438.42019arXiv1802.04767OpenAlexW2963790044WikidataQ127959616 ScholiaQ127959616MaRDI QIDQ2322516

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Publication date: 4 September 2019

Published in: (Search for Journal in Brave)

Abstract: Let $psi$ be a positive function defined near the origin such that $li{m}_{to{0}^{+}}psi(t)=0$. We consider the operator �egin{equation*} T_ heta f(x) = lim_{varepsilon o 0^+} int_varepsilon^1 e^{igamma(t)}f(x-t) frac{dt}{t^{ heta}psi(t)^{1- heta}}, end{equation*} where $gamma$ is a real function with $li{m}_{to{0}^{+}}|gamma(t)|=infty$ and $0lehetale1$. Assuming certain regularity and growth conditions on $psi$ and $gamma$, we show that $T_1$ is of weak type $(1,1)$.

Full work available at URL: https://arxiv.org/abs/1802.04767

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