Recently, Professor Zhu Jianfeng(the corresponding author) from the School of Mathematical Sciences of Huaqiao University(HQU), in collaboration with Liu Jinsong(the first author) from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Petar Menlentijević(the second author) from the University of Belgrade, published an academic paper titled “L^p norm of truncated Riesz transform and an improved dimension-free L^p estimate for maximal Riesz transform”(DOI:10.1007/s00208-023-02736-1) in Mathematische Annalen. He also collaborated with Liu Jinsong(the first author) on another academic paper titled “Riesz conjugate functions theorem for harmonic quasiconformal mappings”(DOI:10.1016/j.aim.2023.109321) in Advances in Mathematics.

The Riesz transforms play an important role in the operator theory. In 2022, Kucharski and Wróbel from Poland proved a dimension-free L^p(R^d), 1<p<∞, estimate for the vector of maximal Riesz transforms of odd order in terms of the corresponding Riesz transforms. In the first paper, Professor Zhu Jianfeng, Liu Jinsong, and Petar Menlentijevićgeneralized and improved their results by using integration by parts formula for radial Fourier multipliers. Moreover, they inferred the L^p norm contractivity of the truncated Riesz transforms Rt j in terms of R_j, and their accurate L^p norms.

“L^p norm of truncated Riesz transform and an improved dimension-free L^p estimate for maximal Riesz transform”

Link to paper: https://doi.org/10.1007/s00208-023-02736-1

Riesz conjugate function theorem is a classical the oremin analytic functions. In 2011, Astala and Koskela questioned if there exists a quasicon formal analog for the Riesz theorem on conjugate functions. In the second paper, Professor Zhu Jianfeng and Liu Jinsong generalized the Riesz conjugate functions theorem for planar harmonic K-quasiregular mappings and harmonic K-quasiconformal mappings in the unit disk.

“Riesz conjugate functions theorem for harmonic quasiconformal mappings”

Link to paper: https://doi.org/10.1016/j.aim.2023.109321

Mathematische Annalen, a top-tier German mathematical research journal with high academic influence founded in 1868, is committed to publishing important breakthroughs in various fields of mathematics. The journal known for its rigorous peer-review processes has published many influential research results. Famous mathematicians Felix Klein and David Hilbert served as the managing editors of the journal, and Albert Einstein, a member of its editorial board, published significant findings in the journal.Advances in Mathematics, a T1 journal of the Chinese Mathematical Society with high academic influence founded in 1961, is dedicated to covering groundbreaking research on pure mathematics.

（Editor: Wei Linying）