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Universal Journal of Mathematics and Mathematical Sciences

Universal Journal of Mathematics and Mathematical Sciences
Volume 11, Issue 2, Pages 77 - 89 (December 2018)
http://dx.doi.org/10.17654/UM011020077

INTEGRABILITY OF ERGODIC SQUARE FUNCTION

Sakin Demir

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.