Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Riesz transform associated with the fractional Fourier transform and
  applications   Since Zayed \cite[Zayed, 1998]{z2} introduced the fractional Hilbert
transform related to the fractional Fourier transform, this transform has been
widely concerned and applied in the field of signal processing. Recently, Chen,
the first, second and fourth authors \cite[Chen et al, 2021]{cfgw} attribute it
to the operator corresponding to fractional multiplier, but it is only limited
to 1-dimensional case. This paper naturally considers the high-dimensional
situation. We introduce the fractional Riesz transform associated with
fractional Fourier transform, in which the chirp function is the key factor and
the technical barriers to be overcome. Furthermore, after equipping with chirp
functions, we introduce and investigate the boundedness of singular integral
operators, the dual properties of Hardy spaces and BMO spaces as well as the
applications of theory of fractional multiplier in partial differential
equation, which completely matched some classical results. Through numerical
simulation, we give the physical and geometric interpretation of the
high-dimensional fractional multiplier theorem. Finally, we present the
application of the fractional Riesz transform in edge detection, which verifies
the prediction proposed in \cite[Xu et al, 2016]{xxwqwy}. Moreover, the
application presented in this paper can also be considered as the
high-dimensional case of the application of the continuous fractional Hilbert
transform in edge detection in \cite[Pei and Yeh, 2000]{py}.

7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn