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For questions regarding harmonic functions.

3 votes
0 answers
118 views

An open problem of Hardy and Littlewood on $p$-integral means

In Duren's book "Theory of $H^p$ spaces" (MSN) in the comment section after Section 4, it is mentioned that Littlewood and Hardy proved in Some properties of conjugate functions that if $u$ is a harmo …
an_ordinary_mathematician's user avatar
1 vote

Pair of positive harmonic functions with negative inner product in Drury-Arveson space

I will try to prove that such functions do not exist. Suppose that $f,g$ are positive (pluri)harmonic functions in the pluri harmonic Drury Arveson space $\mathcal{H}DA_d$ such that $ \langle f ,g \ra …
an_ordinary_mathematician's user avatar
3 votes
0 answers
88 views

Upcrossing lemma and subharmonic functions

I have been studying the upcrossing lemma for submartingales, which asserts that if $X_n$ is a non negative submartingale, and $ \lambda>0$ then if we denote by $U_n$ the number of $[0,\lambda]$-upcro …
an_ordinary_mathematician's user avatar