Muhammad Asad Zaighum

Sharp weighted bounds for one-sided operators

Abstract In this paper, we establish sharp weighted bounds (Buckley-type theorems) for one-sided maximal and fractional integral operators in terms of one-sided A p {A_{p}} characteristics.

Weighted kernel operators in variable exponent amalgam spaces

The paper is devoted to weighted inequalities for positive kernel operators in variable exponent amalgam spaces. In particular, a characterization of a weight v governing the boundedness/compactness of the weighted kernel operators Kv and Kv, defined on R+ and ℝ, respectively, under the log-Hölder continuity condition on exponents of spaces is established. These operators involve, for example, weighted variable parameter fractional integrals. The results are new even for constant exponent amalgam spaces.MSC:46E30, 47B34.

On the boundedness of Marcinkiewicz integrals on continual variable exponent Herz spaces

Abstract In this paper, we obtain the boundedness of the Marcinkiewicz integral on continual Herz spaces with variable exponent, where all parameters defining the space are variable.

On the boundedness of product kernel operators with measures

Abstract. A characterization of the boundedness for multiple kernel operators defined with respect to a product Borel measure on is established. Necessary and sufficient conditions are formulated for the two-weighted (two-measured) inequalities for the multiple Hardy and Riemann–Liouville transforms defined by product measures. A similar result for the strong one-sided fractional maximal operator is also derived. In all cases the target Lebesgue spaces are defined by a measure having, generally speaking, non-product form. As a corollary we have, for example, two-weighted criteria for discrete multiple Hardy transforms. A Fefferman–Stein type inequality for the multiple Riemann–Liouville transform defined with respect to a measure is derived in the diagonal case.