报告人：陈鹏 (中山大学)

邀请人：郑权

报告时间：2023年4月14日（星期五）10:30-11:30

报告地点：科技楼南611室

报告题目：The Garnett--Jones Theorem on BMO spaces associated with operators and applications

报告摘要：Let $X$ be a metric space with doubling measure, and $L$ be a nonnegative self-adjoint operator on $L^2(X)$ whose heat kernel satisfies the Gaussian upper bound.In this talk,  we give a construction  that for every $ f$  in the $ {\rm BMO}_L(X)$ space associated with the operator $L$, we have  comparable upper and lower bounds for the distance$${\rm dist} (f, L^{\infty}):= \inf_{g\in L^{\infty}}  \|f -g\|_{{\rm BMO}_L(X)}$$ by the constant in the John and Nirenberg inequality for the space ${\rm BMO}_L(X)$ space:$$\sup_B { \mu\{ x\in B: |f(x)-e^{-{r_B^2}L}f(x)|>\lambda\}\over \mu(B)}\leq e^{-\lambda/\varepsilon}\ \ \ \ {\rm for\ large\ } \lambda,$$ which  extends the theorem of  Garnett and John \cite{GJ1} for the classical BMO space of John and Nirenberg.We also give a construction that a compact supported $\BMO_L(X)$ function can be decomposed as the summation of a $L^\infty$-function and the integral of the heat kernel with respect to a finite Carleson measure. Random dyadic lattice method is used in both of the two kinds of constructions.

报告人简介：陈鹏，中山大学数学学院副教授；主要从事调和分析的研究；主要学术成果发表在《Math. Ann.》、《Adv. Math.》、《J. Math. Pures Appl.》、《Int. Math. Res. Not. IMRN》、《Trans. Amer. Math. Soc.》、《Math. Z.》、《J. Funct. Anal.》等国际重要数学期刊上；2018年获得教育部自然科学奖一等奖（第3完成人）；先后主持国家自然科学基金面上项目、青年基金项目和广东省自然科学基金面上项目。