• Journal of the Korean Mathematical Society
• /
• v.58 no.2
• /
• pp.383-400
• /
• 2021

The aim of this paper is to mainly establish the sufficient and necessary conditions for the boundedness of the commutator ����Ω,b which is generated by the parameter Marcinkiwicz integral ����Ω and the Lipschitz function b on generalized Orlicz-Morrey space L��,��(Rd) in the sense of the Adams type result (or Spanne type result). Moreover, the necessary conditions for the parameter Marcinkiewizcz integral ����Ω on the L��,��(Rd), and the commutator [b,����Ω] generated by the ����Ω and the space BMO on the L��,��(Rd), are also obtained, respectively.

• Communications of the Korean Mathematical Society
• /
• v.19 no.3
• /
• pp.435-452
• /
• 2004

In this paper, we prove the weighted continuity of multilinear Marcinkiewicz operators for the extreme cases of p.

• Journal of the Korean Mathematical Society
• /
• v.58 no.4
• /
• pp.1035-1058
• /
• 2021

Under certain rather weak size conditions assumed on the kernels, some weighted norm inequalities for singular integral operators, related maximal operators, maximal truncated singular integral operators and Marcinkiewicz integral operators in nonisotropic setting will be shown. These weighted norm inequalities will enable us to obtain some vector valued inequalities for the above operators.

• Journal of the Korean Mathematical Society
• /
• v.42 no.5
• /
• pp.1087-1100
• /
• 2005

In this note we give the mapping properties of the Marcinkiewicz integral !-to. at some end spaces. More precisely, we first prove that !-to. is a bounded operator from H$^{1,($\mathbb{R) to H$^{1, ($\mathbb{R). As a corollary of the results above, we obtain again the weak type (1,1) boundedness of $\mu$$_{, but the condition assumed on n is weaker than Stein's condition. Finally, we show that !-to. is bounded from BMO($\mathbb{R) to BMO($\mathbb{R). The results in this note are the extensions of the results obtained by Lee and Rim recently.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.3
• /
• pp.771-788
• /
• 2015

In this note we consider the parametric Marcinkiewicz integrals with mixed homogeneity along polynomials compound curves. Under the rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction, the $L^p$ bounds of such operators are given by an extrapolation argument. Some previous results are greatly extended and improved.

• Journal of the Korean Mathematical Society
• /
• v.43 no.3
• /
• pp.635-658
• /
• 2006

This paper is concerned with giving some rather weak size conditions implying the $L^P$ boundedness of the multiple Marcin-kiewicz integrals for some fixed $1\;<\;p\;<\;{\infty}$, which essentially improve and extend some known results.

• Kyungpook Mathematical Journal
• /
• v.59 no.2
• /
• pp.259-275
• /
• 2019

The aim of this paper is to prove that Marcinkiewicz integral operators are bounded from ${\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$ to ${\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$ when the parameters ${\alpha}({\cdot})$, $p({\cdot})$ and $q({\cdot})$ satisfies some conditions. Also, we prove the boundedness of ${\mu}$ on variable Herz-type Hardy spaces $H{\dot{K}}^{{\alpha}({\cdot}),q({\cdot})}_{p({\cdot})}({\mathbb{R}}^n)$.