Abstract
We will introduce the times modified centered and uncentered Hardy-Littlewood maximal operators on nonhomogeneous spaces for. We will prove that the times modified centered Hardy-Littlewood maximal operator is weak type bounded with constant when if the Radon measure of the space has "continuity" in some sense. In the proof, we will use the outer measure associated with the Radon measure. We will also prove other results of Hardy-Littlewood maximal operators on homogeneous spaces and on the real line by using outer measures.
Highlights
Hardy-Littlewood maximal operators were first introduced by Hardy and Littlewood ([6]) in one dimensional case for the purpose of the application to Complex Analysis
Nazarov et al ([9]) defined modified Hardy-Littlewood maximal operators on quasi-metric measure spaces possesing a Radon measure that does not satisfy a doubling condition, which are used in harmonic analysis on nonhomogeneous spaces
We will treat weak type (1,1) inequalities satisfied by several types of Hardy-Littlewood maximal operators
Summary
Hardy-Littlewood maximal operators were first introduced by Hardy and Littlewood ([6]) in one dimensional case for the purpose of the application to Complex Analysis. Coifman and Weiss ([4]) defined Hardy-Littlewood maximal operators on quasi-metric measure spaces satisfying doubling conditions (which we call homogeneous spaces). Nazarov et al ([9]) defined modified Hardy-Littlewood maximal operators on quasi-metric measure spaces possesing a Radon measure that does not satisfy a doubling condition (which we call nonhomogeneous spaces), which are used in harmonic analysis on nonhomogeneous spaces. Weak type (1,1) inequalities satisfied by Hardy-Littlewood maximal operators are keys to prove their strong type (p, p) boundedness via Marcinkiewicz’s interpolation theorem. To prove their weak type (1,1) inequalities, the unification of our approach is the use of outer measures.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
