Publications

Book

  • A Sharp Theory of Hardy Spaces on Ahlfors-Regular Quasi-Metric Spaces. With M.Mitrea, Springer Lecture Notes in Mathematics, Vol.2142, (2015), 486 pages. Introduction Purchase

Papers

  • The game of cycles. With M.Averett, B.Gaines, C.Jackson, M.L.Karker, M.A.Marciniak, F.E.Su, and S.Walker (To appear in Amer. Math. Monthly)
  • Sobolev embedding for M^{1,p} spaces is equivalent to a lower bound of the measure. With P.Górka and P.Hajłasz. J. Funct. Anal. 279 (2020), no. 7, 108628
  • A note on metric-measure spaces supporting Poincaré inequalities. With P.Hajłasz. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 31 (2020), no.1, 15-23.
  • Whitney-type extensions with control of the modulus of continuity in geometrically doubling quasi-metric spaces. With I.Mitrea and M.Mitrea. Commun. Pure Appl. Anal., 12 (2013), No. 1, pp. 59-88.
  • Sharp geometric maximum principles for semi-elliptic operators with singular drift. With D.Brigham, V.Maz'ya, M.Mitrea and E.Ziadé, Math. Res. Lett., Vol.18 (2011), No. 04, pp. 613-620. Full Text PDF
  • On the regularity of domains satisfying a uniform hour-glass condition and a sharp version of the Hopf-Oleinik Boundary Point Principle. With D.Brigham, V.Maz'ya, M.Mitrea and E.Ziadé, Journal of Mathematical Sciences, Vol. 176 (2011), No. 3, pp. 281-360.
  • Topics in Harmonic Analysis and Partial Differential Equations: Extension Theorems and Geometric Maximum Principles. Masters Thesis. (2011). Full Text PDF

Preprints

  • Characterizing Lusin's Theorem and the Density of Continuous Functions in Lebesgue Spaces via the Regularity of the Measure. With M.Mitrea and B.Schmutzler.

In Preparation

  • Optimal embeddings and extensions for Hajlasz-Triebel-Lizorkin and Besov spaces. With D.Yang and W.Yuan.
  • Hardy spaces with vanishing moments on metric measure spaces. With D.Brazke and A.Schikorra.
  • Mixed-norm spaces in spaces of homogeneous type. With D.Mitrea, I.Mitrea, and M.Mitrea.
  • On the well-posedness of the Dirichlet Boundary problem for elliptic systems in Lyapunov domains with data in Hölder spaces. With D.Mitrea, M.Mitrea, and B.Schmutzler.