An essential foundational issue in harmonic analysis is comprehending the boundedness features of Fourier multipliers between Banach function spaces. This workshop aims to teach the broad theory of Fourier multipliers on Lebesgue spaces and cover some important tools used in the study, such as maximal functions, singular integrals, and Littlewood-Paley square functions. Applications to PDEs and related subjects like PseudoDifferential Operators, Bi-Linear Fourier Multipliers, Restriction Theorem, and others will also be discussed.

Our program comprises the following research topics:

• Introduction to Fourier Multiplier Operators
• Singular Integrals
• Littlewood-Paley Theory
• Classical Multiplier Results: Hormander-Mihilin and Marcinkiewich Theorems etc.
• Bochner-Riesz and Related Multipliers
• Restriction Theorems and Applications to PDEs
• Bi-linear Fourier Multipliers
• Pseudo-Differential Operators
• H-measure and applications

which have mutual interconnections.

Speakers

• Prof. S. Thangavelu (IISc, Bangalore)
• Prof. E.K. Narayanan (IISc, Bangalore)
• Prof. Parasar Mohanti (IIT Kanpur)
• Prof. Agnid Banerjee (TIFR CAM, Bangalore)
• Prof. Saurabh Kumar Shrivastava (IISER Bhopal)
• Prof. Rahul Garg (IISER Bhopal)
• Prof. Jotsaroop Kaur (IISER Mohali)
• Prof. Ratnakumar P.K. (HRI, Prayagraj)
• Dr. Tuhin Ghosh (HRI, Allahabad)

The workshop is funded by the DAE, India.