Uniform sparse bounds for discrete quadratic phase Hilbert transforms
Uniform sparse bounds for discrete quadratic phase Hilbert transforms
复制标题
离散二次相位希尔伯特变换的均匀稀疏边界
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Darío Mena Arias
中科院分区：
文献类型：
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作者：
R. Kesler;Darío Mena Arias
For each $$alpha in mathbb {T}$$α∈T consider the discrete quadratic phase Hilbert transform acting on finitely supported functions $$f : mathbb {Z}
ightarrow mathbb {C}$$f:Z→C according to $$egin{aligned} H^{alpha }f(n):= sum _{m
e 0} frac{e^{ialpha m^2} f(n - m)}{m}. end{aligned}$$Hαf(n):=∑m≠0eiαm2f(n-m)m.We prove that, uniformly in $$alpha in mathbb {T}$$α∈T, there is a sparse bound for the bilinear form $$leftlangle H^{alpha } f , g
ight
angle $$Hαf,g for every pair of finitely supported functions $$f,g : mathbb {Z}
ightarrow mathbb {C}$$f,g:Z→C. The sparse bound implies several mapping properties such as weighted inequalities in an intersection of Muckenhoupt and reverse Hölder classes.
For each $$alpha in mathbb {T}$$α∈T consider the discrete quadratic phase Hilbert transform acting on finitely supported functions $$f : mathbb {Z}
ightarrow mathbb {C}$$f:Z→C according to $$egin{aligned} H^{alpha }f(n):= sum _{m
e 0} frac{e^{ialpha m^2} f(n - m)}{m}. end{aligned}$$Hαf(n):=∑m≠0eiαm2f(n-m)m.We prove that, uniformly in $$alpha in mathbb {T}$$α∈T, there is a sparse bound for the bilinear form $$leftlangle H^{alpha } f , g
ight
angle $$Hαf,g for every pair of finitely supported functions $$f,g : mathbb {Z}
ightarrow mathbb {C}$$f,g:Z→C. The sparse bound implies several mapping properties such as weighted inequalities in an intersection of Muckenhoupt and reverse Hölder classes.