Smoothing properties of bilinear operators and Leibniz-type rules in Lebesgue and mixed Lebesgue spaces

By Jarod Hart, Rodolfo H. Torres, Xinfeng Wu. Transactions of the American Mathematical Society, 2017

75 citations recorded by the source corpus.

We prove that bilinear fractional integral operators and similar multipliers are smoothing in the sense that they improve the regularity of functions. We also treat bilinear singular multiplier operators which preserve regularity and obtain several Leibniz-type rules in the contexts of Lebesgue and mixed Lebesgue spaces.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2f9c0e9aaaf11b7c3ee59620ad6854b3b8ccf366

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In Applied Mathematics

1. Dachun Yang
2. Wen Yuan
3. Long Huang
4. Jun Liu
5. Yangyang Zhang
6. Yoshihiro Sawano
7. Songbai Wang
8. Ciqiang Zhuo

In Mathematical Physics

1. Dachun Yang
2. Wen Yuan
3. Jun Liu
4. Long Huang
5. Yoshihiro Sawano
6. Ciqiang Zhuo
7. Yangyang Zhang
8. Songbai Wang

Citations in the corpus

• Dual spaces of anisotropic mixed-norm Hardy spaces (2018, background): “In addition, the theory of anisotropic or mixed-norm function spaces was developed well in recent years; see, for example, [6, 7, 9, 14, 18].”
• On Function Spaces with Mixed Norms — A Survey (2019, methodology): “[38] introduced the mixed-norm Hardy space Hp,q(Rn+1) with p, q∈ (0,∞) via the Littlewood– Paley g-function.”