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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
Veröffentlicht/Copyright:
6. April 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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Artikel in diesem Heft
- Attractivity results for a nonlinear functional integral equation
- A biregular extension theorem from a fractal surface in
- Exceptional functions and normal families of holomorphic functions with multiple zeros
- A note on the existence of three positive periodic solutions of functional difference equation
- Necessary and sufficient optimality conditions for set-valued optimization problems
- A weak type inequality for the two-dimensional diagonal Sunouchi operator on the Hardy space
- Screen slant lightlike submanifolds of indefinite cosymplectic manifolds
- Electromagnetic scattering by cylindrical orthotropic waveguide irises
- On fusion frames in Banach spaces
- A note on Muckenhoupt type weight classes on nondoubling measure spaces
- (σ, τ)-amenability of C*-algebras
- Approximation by Nörlund means of Walsh–Kaczmarz–Fourier series
- A priori estimates of solutions of boundary value problems for two-dimensional systems of singular differential inequalities
- Function classes and convergence almost everywhere
- On the equivalence of a strong symmetrical and a strong complete differentiation basis
