报告题目：Riesz-Kolmogorov theorem in the variable exponent Lebesgue spaces and applications

报告人：傅尊伟 教授

邀请人：默会霞 副教授

报告时间：2018年6月19日（星期二）上午 8：40-9：40

报告地点：主楼1214

摘 要：

We obtain the necessary and sufficient condition of the pre-compact sets in the variable exponent Lebesgue spaces, which is also called the Riesz-Kolmogorov theorem. The main novelty appearing in this approach is the constructive approximation and does not rely on the boundedness of the Hardy-Littlewood maximal operator in the considered spaces such that the authors do not need the log-Holder continuous conditions on the variable exponent. As applications, we establish the boundedness of Riemann-Liouville integral operators and prove the compactness of truncated Riemann-Liouville integral operators in the variable exponent Lebesgue spaces. Moreover, applying the Riesz-Kolmogorov theorem, we obtain the existence and the uniqueness of solutions to a Cauchy type problem for fractional differential equations in variable exponent Lebesgue spaces.

报告人简介：

傅尊伟，1977年生，博士，临沂大学数学与统计学院教授，韩国水原大学计算机科学专业博士生导师、山东师范大学数学专业博士生导师，山东省重点学科首席专家、全国优秀教师，美国《数学评论》评论员。发表SCI论文62篇。1篇论文被列入ESI高频引文。先后主持国家自然科学基金青年项目1项、面上项目2项。获得山东省高校优秀科研成果奖一等奖和省级教学成果奖一等奖各1项。2010年应邀在英国剑桥大学举行的“第二届世界青年数学家大会”上做45分钟学术报告。