A new proof of the two weight norm inequality for the one-sided fractional maximal operator

A Hardy type two-weighted inequality is investigated for the multidimensional Hardy operator in the norms of generalized Lebesgue spaces L p(·) . Equivalent necessary and sufficient conditions are found for the L p(·) −→ L q(·) boundedness of the Hardy operator when exponents q(0) < p(0), q(∞) < p(∞). It is proved that the condition for such an inequality to hold coincides with the condition for the validity of two-weighted Hardy inequalities with constant exponents if we require of the exponents to be regular near zero and at infinity. Mathematics Subject Classification (2000). 26D10, 45P05.

show abstract

On a general weighted Hardy type inequality in the variable exponent Lebesgue spaces

Cruz-Uribe

Mamedov

2011

Rev Mat Complut

View full text Add to dashboard Cite

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

A new proof of the two weight norm inequality for the one-sided fractional maximal operator

Abstract: Abstract. We give a new proof of the two weight norm inequality for the one-sided, fractional maximal operator, M + α , simplifying the original proof of Martín-Reyes and de la Torre.

Cited by 4 publications

References 8 publications

Weighted norm inequalities for geometric fractional maximal operators

Weighted norm inequalities for geometric fractional maximal operators

On a Hardy Type General Weighted Inequality in Spaces L p(·)

On a general weighted Hardy type inequality in the variable exponent Lebesgue spaces

Contact Info

Product

Resources

About