Universal Journal of Mathematics and Mathematical Sciences
Volume 11, Issue 2, Pages 77 - 89
(December 2018)
http://dx.doi.org/10.17654/UM011020077 |
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INTEGRABILITY OF ERGODIC SQUARE FUNCTION
Sakin Demir
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Abstract:
Let Sf denote the square function of the difference of ergodic averages over lacunary sequences for an integrable function f. We first prove that S maps a function in ergodic H1 space to a function in L1 space and then we use this result to prove that Sf is integrable if f log+ f is integrable. |
| Keywords and phrases: ergodic square function.
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