The sharp maximal-variation inequality on the integer lattice
Let pe(1/2,1]p e(1/2,1]pe(1/2,1] and let f:ZtomathbbRf:\mathbb{Z}tomathbb{R}f:ZtomathbbR be a function in ellp(Z)ell^{p}(\mathbb{Z})ellp(Z). Write rmVarpf{rm Var}p frmVarpf for the ppp-variation of fff, and let MfMfMf denote the centered discrete…