Sentence examples for pair of weights from inspiring English sources

Segovia and Torrea [11] gave the weighted boundedness of higher order commutator for vector-valued integral operators with a pair of weights using the Rubio de Francia extrapolation idea for weighted norm inequalities.

Let σ and ω be locally finite positive Borel measures on R. Subject to the pair of weights satisfying a side condition, we characterize boundedness of the Hilbert transform H from L2 to L2 in terms of the A2 condition[∫I(|I||I|+|x−xI|)2dω(x)∫I |I||I|+|x−xI| 2dσ(x)]12⩽C|I|, and the two testing conditions: For all intervals I in R∫IH 1Iσ)(x)2dω(x)⩽C∫Idσ(x),∫IH 1Iω)(x)2dσ(x)⩽C∫Idω(x).

[9] Let 0 < α < mn, (u, v) is a pair of weights.

Let be a pair of weights for which there exists such that (2.6).

We say a pair of weights satisfies the -condition in a set, write, for some and with if (3.7).

One says a pair of weights satisfies the -condition, writes, if for all balls, one has that (2.1).

Thus, for a specific pair of weight w and number c, the length l listed in the table should be regarded as the minimum read length that w and c support.

Attraction between pairs of weights caused the wire to twist slightly.

Old sash (or double-hung) windows are counter-balanced by two pairs of weights hidden in each side of the window.

We give several extrapolation theorems for pairs of weights of the form (w, Mkw) and (w, (Mw/w)r w), where w is any non-negative function, r>1, and Mk is the kth iterate of the Hardy Littlewood maximal operator.

They characterized the pairs of weights (u, v) such that the inequality (1.1).