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Invariance of the Gibbs measure for the Benjamin–Ono equation

Yu Deng — 2015

Journal of the European Mathematical Society

In this paper we consider the periodic Benjemin-Ono equation.We establish the invariance of the Gibbs measure associated to this equation, thus answering a question raised in Tzvetkov [28]. As an intermediate step, we also obtain a local well-posedness result in Besov-type spaces rougher than L 2 , extending the L 2 well-posedness result of Molinet [20].

Some results on magic squares based on generating magic vectors and R-C similar transformations

Xiaoyang MaKai-tai FangYu hui Deng — 2017

Special Matrices

In this paper we propose a new method, based on R-C similar transformation method, to study classification for the magic squares of order 5. The R-C similar transformation is defined by exchanging two rows and related two columns of a magic square. Many new results for classification of the magic squares of order 5 are obtained by the R-C similar transformation method. Relationships between basic forms and R-C similar magic squares are discussed. We also propose a so called GMV (generating magic...

Double weighted commutators theorem for pseudo-differential operators with smooth symbols

Yu-long DengZhi-tian ChenShun-chao Long — 2021

Czechoslovak Mathematical Journal

Let - ( n + 1 ) < m - ( n + 1 ) ( 1 - ρ ) and let T a ρ , δ m be pseudo-differential operators with symbols a ( x , ξ ) n × n , where 0 < ρ 1 , 0 δ < 1 and δ ρ . Let μ , λ be weights in Muckenhoupt classes A p , ν = ( μ λ - 1 ) 1 / p for some 1 < p < . We establish a two-weight inequality for commutators generated by pseudo-differential operators T a with weighted BMO functions b BMO ν , namely, the commutator [ b , T a ] is bounded from L p ( μ ) into L p ( λ ) . Furthermore, the range of m can be extended to the whole m - ( n + 1 ) ( 1 - ρ ) .

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