On the HP-LP-boundedness of some integral operators

In this paper we obtain the H-P(R-n) -> L-P(R-n) boundedness, 0 < p <= 1, of integral operators of the form Tf(x) = integral vertical bar x - a(1)y vertical bar(-alpha 1) . . . vertical bar x - a(m)y vertical bar(-alpha m) f(y)dy, alpha(1) + . . . + alpha(m) = n and a(i) is an element of R \ {0}, a(j) not equal a(j) for i not equal j, l <= i, j <= m. We also show that these operators are not bounded on H-p (R).