What question did this study set out to answer?

To develop the Sawyer duality principle for non-increasing functions and extend results to higher dimensions.

April 10, 2026Open Access

On Sawyer Duality in One and Higher Dimensions

Key Points

To develop the Sawyer duality principle for non-increasing functions and extend results to higher dimensions.
Developed a duality principle for non-increasing functions using modified integrals.
Applied Stepanov’s results to establish findings for non-decreasing functions.
Validated results across one and higher dimensions.
Demonstrated a new duality involving integrals of non-increasing functions.
Showed that Stepanov’s results can also apply to non-decreasing functions using the newly developed principle.
Confirmed findings in Rn, extending the scope of both duality principles.

Abstract

We develop the Sawyer duality principle for non-increasing functions where, in the denominator, the function g is replaced by ∫x∞g(t)tdt. This result complements Stepanov’s result in which g was replaced by 1x∫0xg(t)dt. We use our result and obtain Stepanov’s result for non-decreasing functions and similarly use Stepanov’s result in proving our result for non-decreasing functions. These results have also been obtained in Rn.

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Authors

Alberto Fiorenza

Pankaj Jain

S. Mohanty

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Institutions

University of Naples Federico II

Istituto per le Applicazioni del Calcolo Mauro Picone

South Asian University

References and Citations

Connected Papers

Building similarity graph...

Analyzing shared references across papers

On Sawyer Duality in One and Higher Dimensions

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Authors

Journals

Actions

Institutions

References and Citations

Citation Network

Connected Papers

Discussion

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