My advisor gave me the other day a draft of a paper he's been working on to study. The following is only a part of a proof which I am trying to figure out at the moment.
Now since, I'm afraid of asking something too trivial to my advisor, I thought to pose a couple of questions here, hoping you will shed some light on my confusion.
Questions:
- What kind of Poincare inequality is that, in which the derivative lies on the left hand-side?
- Is $\partial_X^{-1} B$ the inverse derivative of B or what?
- Is there any way, one can modify the classical Poincare inequality (see Evans, PDEs, §5.8) using Fourier transform in order to obtain something similar to this?
I have been taught how to solve integral equations using Laplace Transformation and I am also familiar with Fourier analysis in general. However, I'm having a really hard time getting my head around this one.
Many thanks in advance for the understanding and the help!