Thanks, Tony! I’m not sure how I managed to miss that bit of discussion; I’ve read through that particular chapter multiple times. Anyway, thanks again for pointing it out.

]]>I guess the unitary operator on the right hand side is just the identity. And now i feel it satisfies the singular value decomposition and the norm of the operator is the supremum amongst the norm of the column vectors.

I’m sorry i got the eqn 8 and 9 wrong. They are orthogonal in sense, i believe they map the vector to different subspaces of the vector space. I guess that has nothing to do with unitary. Sorry for the wrong correlation i tried to create

]]>I have a question regarding the norm of a block diagonal operator. Eq.8 and Eq. 9 and 10 are if and only if statements? Also i feel if the column vectors of the operator can be normalized such that T=QM where Q is the unitary matrix and M is the diagonal matrix whose diagonal entries are the norms of the column vectors. This is very similar to singular value decomposition (without the unitary operator on the right hand side) where the largest value of M is nothing but the largest norm of the column vector. So is there a way to relate the singular values to the norm of the column vectors? ]]>

Thank you Prof. Tao

]]>Best regards

Joerg

*[Corrected, thanks – T.]*

Could you please write an expository note on Calderon-Zygmund decomposition?

Thanks

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