Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $L^2$ Schr\"{o}dinger maximal estimates associated with finite type
  phases in $\mathbb{R}^2$   In this paper, we establish Schr\"{o}dinger maximal estimates associated with
the finite type phases \[\phi(\xi_1,\xi_2):=\xi^m_1+\xi^m_2,\;(\xi_1,\xi_2)\in
[0,1]^2,\] where $m \geq 4$ is an even number. Following [6], we prove an $L^2$
fractal restriction estimate associated with the surfaces
\[F^2_m:=\{(\xi_1,\xi_2,\phi(\xi_1,\xi_2)):\;(\xi_1,\xi_2)\in [0,1]^2\}\] as
the main result, which also gives results on the average Fourier decay of
fractal measures associated with these surfaces. The key ingredients of the
proof include the rescaling technique from [10], the Bourgain-Demeter $\ell^2$
decoupling inequality, reduction of dimension arguments and induction on
scales.

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The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
3
The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: ao-sci