Displaying similar documents to “The structure of module derivations of C n [ 0 , 1 ] into L p ( 0 , 1 ) ”

Two-parameter Hardy-Littlewood inequality and its variants

Chang-Pao Chen, Dah-Chin Luor (2000)

Studia Mathematica

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Let s* denote the maximal function associated with the rectangular partial sums s m n ( x , y ) of a given double function series with coefficients c j k . The following generalized Hardy-Littlewood inequality is investigated: | | s * | | p , μ ≤ C p , α , β Σ j = 0 ∞ Σ k = 0 ∞ ( j ̅ ) p - α - 2 ( k ̅ ) p - β - 2 | c j k | p 1 / p , where ξ̅=max(ξ,1), 0 < p < ∞, and μ is a suitable positive Borel measure. We give sufficient conditions on c j k and μ under which the above Hardy-Littlewood inequality holds. Several variants of this inequality are also examined. As a consequence, the ||·||p,μ-convergence property...

Nonconvolution transforms with oscillating kernels that map Ḃ 1 0 , 1 into itself

G. Sampson (1993)

Studia Mathematica

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We consider operators of the form ( Ω f ) ( y ) = ʃ - ∞ ∞ Ω ( y , u ) f ( u ) d u with Ω(y,u) = K(y,u)h(y-u), where K is a Calderón-Zygmund kernel and h ∈ L ∞ (see (0.1) and (0.2)). We give necessary and sufficient conditions for such operators to map the Besov space Ḃ 1 0 , 1 (= B) into itself. In particular, all operators with h ( y ) = e i | y | a , a > 0, a ≠ 1, map B into itself.