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Higher summability theorems from the weighted reverse discrete inequalities. (English) Zbl 1524.40003

Summary: Motivated by higher integrability theorems due to Muckenhoupt and Gehring, in this paper we establish some related higher summability results for nonincreasing sequences, verifying the weighted reverse discrete inequalities. Our main result will be proved by employing the weighted Hardy-type inequality designed and proved for this purpose.

MSC:

40A05 Convergence and divergence of series and sequences
26D15 Inequalities for sums, series and integrals
40C99 General summability methods
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