Relations between $H\sp p\sb u$ and $L\sp p\sb u$ in a product space

Jan-Olov Str{ömberg, Richard L. Wheeden
1989 Transactions of the American Mathematical Society  
Relations between Lpu and H¡¡ are studied for the product space R1 x R1 in the case 1 < p < oo and u(xux2) = \Q\(x\)\p\Q2(x2)\pw(xi,X2), where Q\ and Qi are polynomials and w satisfies the Ap condition for rectangles. A description of the distributions in H¡¡ is given. Questions about boundary values and about the existence of dense subsets of smooth functions satisfying appropriate moment conditions are also considered.
doi:10.1090/s0002-9947-1989-0951891-7 fatcat:7iepadwosrephpg5mm6bn6nbxy