Displaying similar documents to “On invariant measures for power bounded positive operators”

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

G. Sampson (1993)

Studia Mathematica

Similarity:

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.

On the characterization of Hardy-Besov spaces on the dyadic group and its applications

Jun Tateoka (1994)

Studia Mathematica

Similarity:

C. Watari [12] obtained a simple characterization of Lipschitz classes L i p ( p ) α ( W ) ( 1 ≥ p ≥ ∞ , α > 0 ) on the dyadic group using the L p -modulus of continuity and the best approximation by Walsh polynomials. Onneweer and Weiyi [4] characterized homogeneous Besov spaces B p , q α on locally compact Vilenkin groups, but there are still some gaps to be filled up. Our purpose is to give the characterization of Besov spaces B p , q α by oscillations, atoms and others on the dyadic groups. As applications, we show a strong capacity inequality...

Origami

Παναγιώτης Τελώνης (1989-1990)

Ευκλείδης Α

Similarity:

On some singular integral operatorsclose to the Hilbert transform

T. Godoy, L. Saal, M. Urciuolo (1997)

Colloquium Mathematicae

Similarity:

Let m: ℝ → ℝ be a function of bounded variation. We prove the L p ( ℝ ) -boundedness, 1 < p < ∞, of the one-dimensional integral operator defined by T m f ( x ) = p . v . ∫ k ( x - y ) m ( x + y ) f ( y ) d y where k ( x ) = ∑ j ∈ ℤ 2 j φ j ( 2 j x ) for a family of functions φ j j ∈ ℤ satisfying conditions (1.1)-(1.3) given below.

The value-distribution of lacunary series and a conjecture of Paley

Takafumi Murai (1981)

Annales de l'institut Fourier

Similarity:

The purpose of this paper is to establish a theorem which answers a conjecture of Paley on the distribution of values of Hadamard lacunary series and which is useful to study the Peano curve property of such series.