Hardy-Littlewood and UMD Banach lattices via Bessel convolution operators (Q2891149)

A Banach space \(X\) is called a UMD space if for \(l<p<\infty\) martingale difference sequences \(d=(d_1,d_2,\dots)\) in \(L^p_{[0,1]}\) are unconditional, i.e. there exists \(C_p>0\) such that \(\|\epsilon_1 d_1+\epsilon_2 d_2+\cdots\|\leq C_p \| d_1 +d_2 +\cdots\|\) whenever \(\epsilon_i,\;i=1,2,\dots\), are numbers in \([-1,1]\).NEWLINENEWLINE In the present paper the authors characterize the Banach lattices having the UMD and the Hardy-Littlewood properties.