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- W3187639743 abstract "Asmar et al. [Note on norm convergence in the space of weak type multipliers. J Operator Theory. 1998;39(1):139–149] proved that the space of weak-type Fourier multipliers acting from Lp into Lp,∞ is continuously embedded into L∞. We obtain a sharper result in the setting of abstract Lorentz spaces Λq(X) with 0<q≤∞ built upon a Banach function space X on Rn. We consider a source space S and a target space T in the class of admissible spaces A:={X,Λq(X):0<q≤∞}. Let MS,T0 denote the space of Fourier multipliers acting from S to T. We show that if the space X satisfies the weak doubling property, then the space MΛq(X),Λ∞(X)0 is continuously embedded into L∞ for every 0<q≤∞. This implies that MS,T0 is a quasi-Banach space for all choices of source and target spaces S,T∈A." @default.
- W3187639743 created "2021-08-16" @default.
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- W3187639743 date "2021-08-01" @default.
- W3187639743 modified "2023-10-16" @default.
- W3187639743 title "A lower estimate for weak-type Fourier multipliers" @default.
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- W3187639743 doi "https://doi.org/10.1080/17476933.2021.1958796" @default.
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