This article may be too technical for most readers to understand.(June 2014) |
In mathematics, the Christ窶適iselev maximal inequality is a maximal inequality for filtrations, named for mathematicians Michael Christ and Alexander Kiselev. [1]
A continuous filtration of is a family of measurable sets such that
For example, with measure that has no pure points and
is a continuous filtration.
Let and suppose is a bounded linear operator for finite . Define the Christ窶適iselev maximal function
where . Then is a bounded operator, and
Let , and suppose is a bounded linear operator for finite . Define, for ,
and . Then is a bounded operator.
Here, .
The discrete version can be proved from the continuum version through constructing . [2]
The Christ窶適iselev maximal inequality has applications to the Fourier transform and convergence of Fourier series, as well as to the study of Schrテカdinger operators. [1] [2]
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cite web}}
: CS1 maint: archived copy as title (
link)
{{
cite web}}
: CS1 maint: archived copy as title (
link)
This article may be too technical for most readers to understand.(June 2014) |
In mathematics, the Christ窶適iselev maximal inequality is a maximal inequality for filtrations, named for mathematicians Michael Christ and Alexander Kiselev. [1]
A continuous filtration of is a family of measurable sets such that
For example, with measure that has no pure points and
is a continuous filtration.
Let and suppose is a bounded linear operator for finite . Define the Christ窶適iselev maximal function
where . Then is a bounded operator, and
Let , and suppose is a bounded linear operator for finite . Define, for ,
and . Then is a bounded operator.
Here, .
The discrete version can be proved from the continuum version through constructing . [2]
The Christ窶適iselev maximal inequality has applications to the Fourier transform and convergence of Fourier series, as well as to the study of Schrテカdinger operators. [1] [2]
{{
cite web}}
: CS1 maint: archived copy as title (
link)
{{
cite web}}
: CS1 maint: archived copy as title (
link)