Fractional Hardy-Sobolev type inequalities for half spaces and John domains

As our main result we prove a variant of the fractional Hardy-Sobolev-Maz'ya inequality for half spaces. This result contains a complete answer to a recent open question by Musina and Nazarov. In the proof we apply a new version of the fractional Hardy-Sobolev inequality that we establish also for more general unbounded John domains than half spaces

MOESM4 of Vitamin C induces specific demethylation of H3K9me2 in mouse embryonic stem cells via Kdm3a/b

Additional file 4: Figure S4. Analysis of H3K9me2 at repetitive elements in ES cells treated with vitamin C. ChIP-qPCR for H3K9me2 in ES cells ± vitamin C at the repetitive element families indicated. ChIP for IgG was performed as a negative control. Data are mean ± SD. Asterisks represent P < 0.05 by t test

MOESM1 of Vitamin C induces specific demethylation of H3K9me2 in mouse embryonic stem cells via Kdm3a/b

Additional file 1: Figure S1. Evaluation of changes in H3 PTMs following vitamin C treatment. A) Western blot for several H3 PTMs in ES cells ± vitamin C. B) Immunofluorescence for H3K9me2 and corresponding DAPI staining in untreated and vitamin C-treated ES cells. Merged images show H3K9me2 in green and DAPI staining in red. H3K9me2 immunofluorescence is also shown in Fig. 1e. Scale bar represents 20 μm

MOESM2 of Vitamin C induces specific demethylation of H3K9me2 in mouse embryonic stem cells via Kdm3a/b

Additional file 2: Figure S2. Analysis of H3K9me2 in G9a and GLP knockout ES cells treated with vitamin C. A) Western blot for H3K9me2 in wild-type parental TT2, G9a knockout, and GLP knockout ES cells ± vitamin C. B) Immunofluorescence for H3K9me2 in GiP ES cells ± vitamin C and untreated wild-type TT2, G9a knockout, and GLP knockout ES cells. GiP ES cells treated with vitamin C show a H3K9me2 staining pattern that is similar to G9a and GLP knockout ES cells. Scale bar represents 20 μm