2:00 pm Thursday, May 4, 2017
Junior Analysis: Exponential integrability of BMO functions by Maria Soria in RLM 10th floor
The space of bounded mean oscillation functions (BMO) arises naturally when studying the boundedness of singular integral operators. Thanks to the Calderon-Zygmund theory, we know that this type of operators are bounded from to , when , from to , when , and from to BMO, when . In this talk, we will focus on the latter case. Our main goal is to prove the John-Nirenberng inequality, which is mainly based on the fact that the averages of a BMO function over dyadic cubes only grow at most linearly, while the scale of the cubes shrinks exponentially. As an inmediate consequence, it will follow that functions with mean bounded oscillation have exponential integrability. Submitted by
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