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( H p , L p ) -type inequalities for the two-dimensional dyadic derivative

Ferenc Weisz (1996)

Studia Mathematica

It is shown that the restricted maximal operator of the two-dimensional dyadic derivative of the dyadic integral is bounded from the two-dimensional dyadic Hardy-Lorentz space H p , q to L p , q (2/3 < p < ∞, 0 < q ≤ ∞) and is of weak type ( L 1 , L 1 ) . As a consequence we show that the dyadic integral of a ∞ function f L 1 is dyadically differentiable and its derivative is f a.e.

A class of Fourier multipliers on H¹(ℝ²)

Michał Wojciechowski (2000)

Studia Mathematica

An integral criterion for being an H 1 ( 2 ) Fourier multiplier is proved. It is applied in particular to suitable regular functions which depend on the product of variables.

A Hardy space related to the square root of the Poisson kernel

Jonatan Vasilis (2010)

Studia Mathematica

A real-valued Hardy space H ¹ ( ) L ¹ ( ) related to the square root of the Poisson kernel in the unit disc is defined. The space is shown to be strictly larger than its classical counterpart H¹(). A decreasing function is in H ¹ ( ) if and only if the function is in the Orlicz space LloglogL(). In contrast to the case of H¹(), there is no such characterization for general positive functions: every Orlicz space strictly larger than L log L() contains positive functions which do not belong to H ¹ ( ) , and no Orlicz space...

A Marcinkiewicz type multiplier theorem for H¹ spaces on product domains

Michał Wojciechowski (2000)

Studia Mathematica

It is proved that if m : d satisfies a suitable integral condition of Marcinkiewicz type then m is a Fourier multiplier on the H 1 space on the product domain d 1 × . . . × d k . This implies an estimate of the norm N ( m , L p ( d ) of the multiplier transformation of m on L p ( d ) as p→1. Precisely we get N ( m , L p ( d ) ) ( p - 1 ) - k . This bound is the best possible in general.

A Note on Div-Curl Lemma

Gala, Sadek (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 42B30, 46E35, 35B65.We prove two results concerning the div-curl lemma without assuming any sort of exact cancellation, namely the divergence and curl need not be zero, and d i v ( u v ) H 1 ( R d ) which include as a particular case, the result of [3].

A strong convergence theorem for H¹(𝕋ⁿ)

Feng Dai (2006)

Studia Mathematica

Let ⁿ denote the usual n-torus and let S ̃ u δ ( f ) , u > 0, denote the Bochner-Riesz means of order δ > 0 of the Fourier expansion of f ∈ L¹(ⁿ). The main result of this paper states that for f ∈ H¹(ⁿ) and the critical index α: = (n-1)/2, l i m R 1 / l o g R 0 R ( | | S ̃ u α ( f ) - f | | H ¹ ( ) ) / ( u + 1 ) d u = 0 .

A wavelet characterization for weighted Hardy spaces.

Si Jue Wu (1992)

Revista Matemática Iberoamericana

In this article we give a wavelet area integral characterization for weighted Hardy spaces Hp(ω), 0 &lt; p &lt; ∞, with ω ∈ A∞. Our wavelet characterization establishes the identification between Hp(ω) and T2p (ω), the weighted discrete tent space, for 0 &lt; p &lt; ∞ and ω ∈ A∞. This allows us to use all the results of tent spaces for weighted Hardy spaces. In particular, we obtain the isomorphism between Hp(ω) and the dual space of Hp'(ω), where 1&lt; p &lt; ∞ and 1/p +...

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