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Thus, we see that a square function inequality much like that of (2.13) holds; this completes the proof of Rubio de Francia’s Theorem in the one- dimensional case, aside from the
We can now finish the proof of Proposition 9.12.. This shows the injectivity of β and finishes the proof of Proposition 9.12. These groups correspond to W-groups for p -adic fields,
In this paper, we introduce the Orlicz sequence spaces generated by Ces` aro mean of order one associated with a fixed multiplier sequence of non-zero scalars.. Furthermore,
The proof of the following theorem known till now is based on the martingale theory (see e.g. We give a \pure dyadic analysis" proof for it.. Theorem 5. [AVD]), then can be
In this table we summarize the sequences from the Encyclo- pedia found to be exactly realizable, together with the corresponding sequence counting the orbits, and any other
In Section 3, we collect some basic results in the theory of integral inequalities that we need in the proof of our theorems.. In Section 4, we take up the simpler situation in
A number of adjustment indices, that measure the relative conservatism in the level of published profit, have been developed and these provide a conversion multiplier metric
We will prove the twice continuous differentiability of these two different kinds of ruin probability and present their explicit expressions when the claims are