Higer-order commutators of parametrized Marcinkewicz integrals on Herz spaces with variable exponent
EASL-Vol. 3 (2020), Issue 1, pp. 56 – 70 Open Access Full-Text PDF
Omer Abdalrhman, Afif Abdalmonem, Shuangping Tao
Abstract: Let \(0<\rho<n\) and \(\mu_{\Omega}^{\rho}\) be the Parametrized Marcinkiewicz integrals operator. In this work, the bondedness of \(\mu_{\Omega}^{\rho}\) is discussed on Herz spaces \(\dot{K}_{p(\cdot)}^{\alpha,q(\cdot)}(\mathbb{R}^{n})\), where the two main indices are variable exponent. The boundedness of the commutators generated by BOM function, Lipschitz function and parametrized Marcinkiewicz integrals operator is also discussed.