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Our aim in this paper is to deal with integrability of maximal functions for Herz–Morrey spaces on the unit ball with variable exponent
and for double phase functionals
is nonnegative, bounded and Hölder continuous of order
. We also establish Sobolev type inequality for Riesz potentials on the unit ball.
This study examined whether the occurrence of late neck metastasis in early tongue squamous cell carcinoma can be predicted by evaluating HMGB1 (high mobility group box 1) expression in the primary lesion.
A case–control study was conducted. The cases comprised 10 patients with late neck metastasis. The controls consisted of 16 patients without recurrence. All were examined immunohistochemically for HMGB1 protein expression. The odds ratio for late neck metastasis in relation to HMGB1 was estimated.
Results for HMGB1 were dichotomised into positive staining scores (score, 5–7) and negative scores (0–4). Six cases (60 per cent) and four controls (25 per cent) were HMGB1-positive. Although no significant result was seen, compared with HMGB1-negative patients the odds ratio for late neck metastasis in HMGB1-positive patients was 3.8 (95 per cent confidence interval, 0.6–26.5) after adjusting for other factors.
In the present study, immunohistochemical study of HMGB1 in early tongue squamous cell carcinoma did not appear to be very useful for predicting occult neck metastasis. Further study is necessary to clarify the relationship between HMGB1 expression and late neck metastasis in early tongue squamous cell carcinoma.
Our aim in this paper is to deal with Sobolev's embeddings for Sobolev–Orlicz functions with ∇u ∈ Lp(·) logLq(·)(Ω) for Ω ⊂ n. Here p and q are variable exponents satisfying natural continuity conditions. Also the case when p attains the value 1 in some parts of the domain is included in the results.
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