Extra Form
Lecturer 김준일
Dept. 연세대 수학과
date Apr 04, 2019

The spherical average has been a source of many problems in harmonic analysis.
Since late 90's,  the study of  the maximal spherical means on the Heisenberg group $mathbb{H}^n$ has been started to show  the pointwise ergodic theorems on the    groups. 
Later, it has turned out to be connected with the fold singularities of the Fourier integral operators, which leads to   the $L^p$ boundedness of the spherical maximal means on the Heisenberg group $mathbb{H}^n$ for $nge 2$.
In this talk, we discuss about the $L^p$ boundedness of the circular maximal function on the Heisenberg group $mathbb{H}^1$. The proof is based on the the square sum estimate of the Fourier integral operators associated with the torus   arising from the vector fields of the Heisenberg group algebra.
We compare this  torus with the characteristic cone of the Euclidean space.

Attachment '1'
  1. 2021-2 Rookies Pitch: Probability Theory (조수빈)

  2. Ill-posedness for incompressible Euler equations at critical regularit

  3. 2021-2 Rookies Pitch: Low Demensional Topology (이동수)

  4. 2021-2 Rookies Pitch: Geometric Topology (김경로)

  5. 허준이 교수 호암상 수상 기념 강연 (Lorentzian Polynomials)

  6. 2021-1 Rookies Pitch: Number Theory (김예슬)

  7. 2021-1 Rookies Pitch: Representation Theory (최승일)

  8. 2021-1 Rookies Pitch: Optimization Theory (이다빈)

  9. 2021-1 Rookies Pitch: Topological Combinatorics (이강주)

  10. 2021-1 Rookies Pitch: PDE, Regularity Theory (박진완)

  11. 2021-1 Rookies Pitch: PDE, Dynamical Systems (박한솔)

  12. 2021-1 Rookies Pitch: Financial Mathematics(전재기), PDE, Kinetic Equation(배기찬)

  13. 2021-1 Rookies Pitch: Algebraic Combinatorics(이승재), Algebraic Geometry(조창연)

  14. <정년퇴임 기념강연> 수학의 시대정신(?)

  15. <학부생을 위한 ɛ 강연> Mathematical Aspects of Machine Learning and Deep Learning AI

  16. Lie group actions on symplectic manifolds

  17. Mathematics, Biology and Mathematical Biology

  18. Quantitative residual non-vanishing of special values of various L-functions

  19. 22Oct

    Classification of simple amenable operator algebras

  20. Quantum Dynamics in the Mean-Field and Semiclassical Regime

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