The paper deals with dimension-controllable (tractable) embeddings of Besov spaces on $n$-dimensional cubes into Zygmund spaces.

A homogeneity property for some Besov spacesBp,qsis proved. An analogous property for someFp,qsspaces is already known.

В статье рассматрива ются анизотропные пр остранства Бесова и Соболева на п лоскости и на единичном кругеК. Дается описание то чных следов этих пространств на п лоских кривых и, в частности, на окруж ностидК.

В статье рассматрива ются анизотропные пр остранства Бесова и Соболева н а плоскости и на единич ном круге, где 1<р<∞ и И . Основная цель состои т в доказательстве анизотропных нераве нств Харди и в изучени и соответствующих про странств и типа Бесова—Соболе ва. Эти результаты буд ут использованы во втор ой работе для точного описания следов упом янутых пространств н а плоских кривых.

Function spaces of type Bs pq and Fs pq cover as special cases classical and fractional Sobolev spaces, classical Besov spaces, Holder- zgmund spaces and inhomogeneous Hardy spaces. In the last or 3 decades they haven been studied preferably on Rn and in mooth bounded domains in Rn including numerous applications to pseudodi_erential operators, elliptic boundary value problems etc. To a lesser extent spaces of this type have been considered in Lipschitz domains. But in recent times there is a growing interest to study and to use spaces of this type in Lipschitz domains and on their boundaries. It is the aim of this paper to deal with function spaces of Bs pq and Fs pq type in Lipschitz domains and on Lipschitz manifolds in a systematic (although not comprehensive) way: We describe and comment on known results, seal some gaps, give new proofs, and add a few new results of relevant aspects.

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Binding to DNA and synthetic duplex polymers of two bifunctional netropsins and effects on supercoiled plasmid DNA as well as their inhibitory potency on DNA topoisomerases have been investigated. Characteristic differences were found in the DNA binding properties of the two bis-netropsins containing a cis and trans tether as reflected by CD, thermal melting and sedimentation measurements. CD results indicate, that the bis-netropsins interact with DNA by a two-step binding mode depending on the ligand concentration. The trans bis-netropsin may form stable complexes with different DNA's at high salt concentration, whereas for cis bis-netropsin DNA complexes the second binding step is completely abolished. The variations in the DNA binding ability of trans and cis bis-netropsin show a close relationship to the differences observed in their inhibitory effects on DNA topoisomerases. It appeared that trans bis-netropsin more strongly blocks topoisomerase activity than the cis isomer and represents the most potent inhibitor of DNA gyrase. Differences in the DNA. binding ability of the bis-netropsins and their inhibitory potency on topoisomerase activity are explained in terms of bidentate and monodentate binding mode of the trans and cis isomer, respectively.

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Sedimentation velocity techniques have been used to study the effect of the antibiotic drug netropsin (Nt) on the structural properties of different forms of closed circular DNA. Nt removes supercoils upon interaction with positively supercoiled DNA and introduces negative supercoils upon binding to relaxed DNA. Applying the classic assay of DNA unwinding by ethidium to complexes of negatively supercoiled DNA with Nt, we found that, compared with naked DNA, more ethidium is needed to convert the Nt-DNA complex into a superhelix-free form. From the shift in the critical ethidium/nucleotide binding ratio, a Nt-mediated decrease in the linking number difference and superhelix density (or increase in the number of superhelical turns) of negatively supercoiled DNA is calculated, synonymous with an increase in the linking number and a decrease in the helical repeat of the relaxed form. A significant influence of the presence of intrinsic bends in the DNA duplex on the magnitude of the drug-induced alterations in DNA supercoiling could not be detected.

The assay of DNA unwinding by ethidium, followed by sedimentation velocity techniques, was applied to complexes of supercoiled plasmid DNA with different non-intercalating drugs which strongly and sequence-specifically bind to DNA. Compared with the behaviour of naked DNA, most of the complexes exhibit an increase in the critical EB/nucleotide binding ratio associated with the principal minimum in the sedimentation profile. Using netropsin (Nt) as the paradigm of the minor groove binders investigated, the drug-induced alterations in various structural parameters of both the relaxed and supercoiled form of DNA are described. Whereas winding number, helical repeat (both being defined with reference to a surface normal), and linking number of the superhelical DNA remain constant in our experiments, its twist number, surface twist, number of superhelical turns as well as the absolute values of linking number difference, superhelix density, and writhing number increase on binding of Nt. Correspondingly, compared with the naked relaxed DNA a higher linking number (or twist number, or winding number), a higher average duplex winding angle and a lower helical repeat have to be assigned to the relaxed Nt-DNA complex. The various minor groove binders investigated were found to differ considerably in their efficiency to alter the structure of supercoiled DNA.

The binding to supercoiled plasmid DNA as well as to double-stranded short DNA fragments of the DNA binding protein. ASBIII, from S. hygroscopicus has been demonstrated by gel retardation asay. As further revealed by sedimentation analysis, the protein-DNA complex formation also involves condensation of DNA and an aggregation step at higher total protein-to-DNA ratio (w/w). In vitro studies of the transcriptional activity of DNA-protein complexes showed that the ASBIII protein inhibits the overall template activity in the RNA polymerase II system to nearly similar extents for various DNA's. Preincubation of ASBIII-DNA complexes of different GC content, however, suggested a selective inhibitory effect on GC-rich DNA due to the higher stability of this complex. The results also indicate that the initiation of transcription of the GC-rich DNA template is affected by the ASBIII protein. The present results on the DNA binding properties and inactivation of the transcription of the ASBIII protein suggest that this protein may be a potential candidate for the local compaction of chromosomal DNA in Streptomyces hygroscopicus.

Comparative sedimentation, diffusion and circular dichroism (c.d.) measurements have been performed on two histones H1 from sperm of the sea urchin Strongylocentrotus intermedius (H1S) and from calf thymus (H1T), at a high salt concentration of 2 m NaCl. Both the Stokes radius and the frictional ratio derived from the hydrodynamic parameters were found to be somwhat smaller for H1S than the corresponding values for H1T. In view of the considerably higher molar mass of H1S compared with that of H1T, this result indicates that H1S in 2 m NaCl has a more compact conformation than H1T, probably due to a higher degree of secondary structure in the flanking domains of H1S. The c.d. measurements likewise show that H1S has a higher content of ordered structures than H1T. Model considerations indicate that the C-terminal tail of H1S is the main candidate for accomodation of these additional secondary structure regions.

We discuss several types of means on Riemannian (globally symmetric) manifolds, hyperbolic manifolds and Lie groups, their mutual interrelations and related function spaces.