$B-$MAXIMAL OPERATORS, $B-$SINGULAR INTEGRAL OPERATORS AND $B-$RIESZ POTENTIALS IN VARIABLE EXPONENT LORENTZ SPACES

Abstract

In this paper, we prove the boundedness of $B-$maximal operator,
$B-$singular integral operators and $B-$Riesz potentials in the variable exponent Lorentz spaces
$L_{p(\cdot),q(\cdot)}(\mathbb{R}^{n}_{k,+})$. As a consequence of the boundedness of
$B-$Riesz potentials in variable exponent Lorentz spaces, we also obtain that
$B-$fractional maximal operators are bounded in
$L_{p(\cdot),q(\cdot)}(\mathbb{R}^{n}_{k,+})$.