Fundamental Properties of Muckenhoupt and Gehring Weights on Time Scales

Abstract

Some fundamental properties of the Muckenhoupt class Ap of weights and the Gehring class Gq of weights on time scales and some relations between them will be proved in this paper. To prove the main results, we will apply an approach based on proving some properties of integral operators on time scales with powers and certain mathematical relations connecting the norms of Muckenhoupt and Gehring classes. The results as special cases cover the results for functions following David Cruz-Uribe, C. J. Neugebauer, and A. Popoli, and when the time scale equals the positive integers, the results for sequences are essentially new.

Norm and Numerical Radius Inequalities for Sums of Power Series of Operators in Hilbert Spaces

“…These concepts are used in different parts of mathematics. Previous research, including the studies referenced in [1][2][3][4][5][6][7][8][9][10], has extensively investigated mathematical inequalities and discovered significant findings. These studies provide a foundation for future research in this field.…”