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A weak type inequality for the two-dimensional diagonal Sunouchi operator on the Hardy space
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Ushangi Goginava
Published/Copyright:
April 6, 2011
Abstract
Define the two dimensional diagonal Sunouchi operator
where S2n, 2n ƒ and σ2n ƒ are the (2n, 2n)th cubic-partial sums and 2nth Marcinkiewicz–Fejér means of a two-dimensional Walsh–Fourier series. The main aim of this paper is to prove that the operator 
is bounded from the Hardy space H1/2 to the weak L1/2 space and is not bounded from the Hardy space H1/2 to the space L1/2.
Received: 2009-02-25
Published Online: 2011-04-06
Published in Print: 2011-March
© de Gruyter 2011
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