ABSOLUTELY SUMMING OPERATORS AND ATOMIC DECOMPOSITION IN BI-PARAMETER HARDY SPACES

作者：Mueller Paul F X; Penteker Johanna

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145(3): 1221-1230.

DOI：10.1090/proc/13300

For f is an element of H-p(delta(2)), 0 < p <= 2, with Haar expansion f = Sigma f(I) x (J)h(I) x (J) we constructively determine the Pietsch measure of the 2-summing multiplication operator
Mf : l infinity -> Hp(delta 2), (phi I xJ) bar right arrow Sigma phi I x JfI x JhI x J
Our method yields a constructive proof of Pisier's decomposition of f is an element of H-p(delta(2))
vertical bar f vertical bar = vertical bar x vertical bar(1-theta)vertical bar y vertical bar(theta) and parallel to x parallel to(1-theta)(X0) parallel to y parallel to(theta)(H2(delta 2)) <= C parallel to f parallel to(Hp(delta 2)),
where X-0 is Pisier's extrapolation lattice associated to H-p(delta(2)) and H-2(delta(2)). Our construction of the Pietsch measure for the multiplication operator M-f involves the Haar coefficients of f and its atomic decomposition. We treated the one-parameter H-p-spaces in Houston Journal Math. 41 (2015), 639-668.

• 出版日期2017-3