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Ding, "[L.sup.2] boundedness for commutator of rough singular integral with variable kernel," Revista Matematica Iberoamericana, vol.
The filter estimate (5.2g) yields the boundedness of [[psi].sub.E].
By noting that, with the boundedness of [E.sub.Si], [[xi].sub.Si], the signal [s.sub.i] in (30) is bounded by [chi] + [square root of 2[kappa]], define the vector as
Moreover, the dead zone inputs are shown in Figures 5 and 6, which explain the boundedness of the dead zone inputs.
This paper assumes that external disturbance and its boundedness are unknown.
This section is based on the decompositions of f [member of] [H[??].sup.[alpha],p.sub.q,L]([R.sup.n]) in the previous section; as applications, we give some boundedness of sublinear operators satisfying certain conditions on Herz-type Hardy spaces associated with operator.
Then, since in this case we have [mathematical expression not reproducible] and 0 [less than or equal to] [[alpha].sub.p] [??] 1, defining the norms according to (2.5), the boundedness of both [mathematical expression not reproducible] and (div u, q) + (div v, q) are obvious again.
By (19), (44), and the boundedness of [OMEGA], we see that
Hence, the boundedness of solutions to chemotactical systems is of particluar interest.
The boundedness of the conjugate operator [15] implies the required inequality
In particular, for some works on the stability and boundedness in certain Volterra integro- differential equations without delay, we referee the interested reader to the papers of Becker ([1], [2], [3]), Burton ([4], [5], [6]), Burton et al.