[spector]

Associate Professor, Okinawa Institute of Science and Technology

**Email:** *daniel.spector AT oist.jp*

**Home-page:** https://groups.oist.jp/nonlinearanalysis

- D. Spector - C. B. Stockdale (Preprint)

On the dimensional weak-type $(1,1)$ bound for Riesz transforms (2020) - D. Spector - S. J. Spector (Preprint)

BMO and Elasticity: Korn's Inequality; Local Uniqueness in Tension (2020) - Á. D. Martínez - D. Spector (preprint)

An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces (2020) - F. Hernandez - D. Spector (preprint)

Fractional Integration and Optimal Estimates for Elliptic Systems (2020) - D. Spector - S. J. Spector (preprint)

Taylor's Theorem for Functionals on BMO with Application to BMO Local Minimizers (2020) - B. Raita - D. Spector (Preprint)

A Note on Estimates for Elliptic Systems with $L^1$ Data (2019) - S. Krantz - M. Peloso - D. Spector (Preprint)

Some remarks on $L^1$ embeddings in the subelliptic setting (2019) - D. Spector (preprint)

New Directions in Harmonic Analysis on $L^1$ (2019) - D. Spector (preprint)

A Noninequality for the Fractional Gradient (2019) - I. Shafrir - D. Spector (Preprint)

Best constants for two families of higher order critical Sobolev embeddings (2018) - D. Spector (preprint)

An Optimal Sobolev Embedding for $L^1$ (2018) - A. Ponce - D. Spector (Preprint)

A decomposition by non-negative functions in the Sobolev space $W^{k, 1}$ (2018) - A. Schikorra - T. T. Shieh - D. Spector (
*Commun. Contemp. Math.*)

Regularity for a fractional $p$-Laplace equation (2018) - D. Spector - J. Van Schaftingen (Preprint)

Optimal embeddings into Lorentz spaces for some vector differential operators via Gagliardo's lemma (2018) - T. T. Shieh - D. Spector (
*Adv. Calc. Var.*)

On a new class of fractional partial differential equations II (2018) - D. Spector - S. Spector (Preprint:
*Arch. Ration. Mech. Anal.*)

Uniqueness of Equilibrium with Sufficiently Small Strains in Finite Elasticity (2018) - N. Fusco - D. Spector (Preprint)

A Remark on an Integral Characterization of the Dual of BV (2017) - A. Ponce - D. Spector (Preprint)

A Boxing Inequality for the Fractional Perimeter (2017) - J. Goodman - D. Spector (Preprint)

Some remarks on boundary operators of Bessel extensions (2017) - A. Ponce - D. Spector (Preprint)

A note on the Fractional Perimeter and Interpolation (2017) - D. Spector (Preprint)

A note on the sublinear Sobolev inequality (2016) - D. Spector - A. Ponce (Preprint)

On formulae decoupling the total variation of BV functions (2016) - A. Schikorra - T. T. Shieh - D. Spector (Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.)

$L^p$-theory for fractional gradient PDE with VMO coefficients (2015) - D. Spector (Preprint)

On a generalization of $L^p$-differentiability (2015) - R. Garg - D. Spector (C. R. Acad. Sci. Paris Sér. I Math.)

On regularity of solutions to Poisson's equation (2014) - G. Psaradakis - D. Spector (J. Funct. Anal.)

A Leray-Trudinger Inequality (2014) - D. Spector (Accepted Paper:
*C. R. Acad. Sci. Paris Sér. I Math*)

$L^p$-Taylor approximations characterize the Sobolev space $W^{1,p}$ (2014) - R. Garg - D. Spector (Accepted Paper:
*Indiana Univ. Math. J.*)

On the role of Riesz potentials in Poisson's equation and Sobolev embeddings (2014) - A. Schikorra - D. Spector - J. Van Schaftingen (Rev. Mat. Iberoam.)

An $L^1$-type estimate for Riesz potentials (2014) - J. Lellmann - K. Papafitsoros - C. Schönlieb - D. Spector (Accepted Paper:
*SIAM J. Imaging Sci.*)

Analysis and Application of a Non-Local Hessian (2014) - D. Spector - T. Mengesha (Accepted Paper:
*Calc. Var. and PDE*)

Localization of Nonlocal Gradients in Various Topologies (2013) - T. T. Shieh - D. Spector (Accepted Paper:
*Adv. Calc. Var.*)

On a new class of fractional partial differential equations (2013) - G. Leoni - D. Spector (
*Journal of Functional Analysis*)

Characterization of Sobolev and BV spaces (2011) - D. Spector (Accepted Paper:
*Proc. Amer. Math. Soc.*)

Simple proofs of some results of Reshetnyak (2010)

*29 oct 2018 - 31 oct 2018:*Workshop “New developments in PDEs and related topics”*8 feb 2016 - 12 feb 2016:*School and Workshop "PDEs and applications"

*7 apr 2021 - 21 apr 2021:*Lecture Series "Slicing and fine properties of $BV^{\mathcal A}$ functions"