On the Hp-Lp boundedness of some integral operators

ROCHA PABLO, URCIUOLO MARTA

GEORGIAN MATHEMATICAL JOURNAL

HELDERMANN VERLAG

Año: 2010

1072-947X

In this paper we obtain the Hp(Rn) - Lp(Rn) boundedness, 0 < p <= 1 of integral operators of the form   Tf(x) = int | x - a_1 y |^{-b_1} ... | x - a_m y |^{-b_m} f(y) dy where a_j ´s are real numbers nonzero, with a_j different from a_i, for i different fron j, i=1, ..., m, j=1,...,m, and b_1 + ... + b_m = n. We also show that these operators are not bounded on Hp(R) where a_j ´s are real numbers nonzero, with a_j different from a_i, for i different fron j, i=1, ..., m, j=1,...,m, and b_1 + ... + b_m = n. We also show that these operators are not bounded on Hp(R) where a_j ´s are real numbers nonzero, with a_j different from a_i, for i different fron j, i=1, ..., m, j=1,...,m, and b_1 + ... + b_m = n. We also show that these operators are not bounded on Hp(R) where a_j ´s are real numbers nonzero, with a_j different from a_i, for i different fron j, i=1, ..., m, j=1,...,m, and b_1 + ... + b_m = n. We also show that these operators are not bounded on Hp(R)