Papers
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B.D., Michał Kijaczko.
On density of smooth functions in weighted fractional Sobolev spaces. Nonlinear Anal. 205 (2021), 10 pp.
arXiv:2009.00077
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B.D., Moritz Kassmann.
Regularity estimates for elliptic nonlocal operators. Anal. PDE 13 (2020), no. 2, 317–370.
arXiv:1509.08320
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B.D., Moritz Kassmann.
Function spaces and extension results for nonlocal Dirichlet problems. J. Funct. Anal. 277 (2019), no. 11, 108134, 22 pp.
arXiv:1612.01628
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B.D., Lizaveta Ihnatsyeva, Juha Lehrbäck, Heli Tuominen, Antti V. Vähäkangas.
Muckenhoupt Ap-properties of distance functions and applications to Hardy-Sobolev–type inequalities.
Potential Anal. 50 (2019), no. 1, 83–105.
arXiv:1705.01360
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B.D.; Juha Lehrbäck, Antti V. Vähäkangas.
Fractional Hardy-Sobolev type inequalities for half spaces and John domains.
Proc. Amer. Math. Soc. 146 (2018), no. 8, 3393–3402.
arXiv:1709.03296
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B.D., Alexey Kuznetsov, Mateusz Kwaśnicki.
Eigenvalues of the fractional Laplace operator in the unit ball.
J. Lond. Math. Soc. (2) 95 (2017), no. 2, 500–518.
arXiv:1509.08533
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B.D., Alexey Kuznetsov, Mateusz Kwaśnicki.
Fractional Laplace operator and Meijer G-function.
Constr. Approx. 45 (2017), no. 3, 427–448.
doi: 10.1007/s00365-016-9336-4,
arXiv:1509.08529
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B.D., Julian Tugaut.
Exponential rate of convergence independent from the dimension in a mean-field system of particles.
Probab. Math. Statist. 37 (2017), no. 1, 145–161.
pdf
preprint
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B.D., Lizaveta Ihnatsyeva, Antti V. Vähäkangas.
On improved fractional Sobolev-Poincaré inequalities.
Ark. Mat. 54 (2016), no. 2, 437–454.
doi: 10.1007/s11512-015-0227-x,
arXiv:1312.5118.
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Krzysztof Bogdan, B.D., Panki Kim.
Hardy inequalities and non-explosion results for semigroups.
Potential Anal. 44 (2016), no. 2, 229–247.
doi: 10.1007/s11118-015-9507-0
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Krzysztof Bogdan, B.D., Tomasz Luks.
On Hardy spaces of local and nonlocal operators.
Hiroshima Math. J. 44 (2014), no. 2, 193-215.
pdf
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B.D., Antti V. Vähäkangas.
Characterizations for fractional Hardy inequality.
Adv. Calc. Var. 8 (2015), no. 2, 173–182.
doi: 10.1515/acv-2013-0019,
arXiv:1308.1886
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B.D., Antti V. Vähäkangas.
A framework for fractional Hardy inequalities.
Ann. Acad. Sci. Fenn. Math. 39 (2014), 675-689.
pdf.
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B.D., Moritz Kassmann.
On weighted Poincaré inequalities.
Ann. Acad. Sci. Fenn. Math. 38 (2013), 721-726; doi: 10.5186/aasfm.2013.3834.
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B.D.
Fractional calculus for power functions.
Fract. Calc. Appl. Anal. 15 (2012), no. 4, 536–555;
doi: 10.2478/s13540-012-0038-8,
arXiv:1103.3387v1
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B.D., Rupert L. Frank.
Fractional Hardy-Sobolev-Maz'ya inequality for domains.
Stud. Math. 208, No. 2, 151-166 (2012),
doi: 10.4064/sm208-2-3,
arXiv:1109.6570v1
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B.D.
The fractional Hardy inequality with a remainder term.
Colloq. Math. 122 (2011), 59-67.
arXiv:0907.4448v2,
doi: 104064/cm122-1-6.
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Krzysztof Bogdan, B.D.
The best constant in a fractional Hardy inequality,
Math. Nachr. 284 (2011), no. 5-6, 629–638; doi: 10.1002/mana.200810109,
arXiv:0807.1825v1
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B.D.
Embedding theorems for Lipschitz and Lorentz spaces on lower Ahlfors regular sets.
Studia Math. 197 (2010), 247-256.
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B.D.; Tadeusz Kulczycki. Spectral gap for stable process on convex planar double symmetric domains. Potential Anal. 27 (2007), no. 2, 101--132.
MR2322501,
arXiv:math/0610283v1.
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B.D. On comparability of integral forms. J. Math. Anal. Appl. 318 (2006), no. 2, 564--577.
MR2215170
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B.D.
A fractional order Hardy inequality.
Illinois J. Math. 48 (2004), no. 2, 575--588.
MR2085428
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Krzysztof Bogdan, B.D.
Relative Fatou theorem for harmonic functions of rotation invariant stable processes in smooth domains.
Studia Math. 157 (2003), no. 1, 83--96.
MR1980119
Preprints
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B.D., Moritz Kassmann.
Comparability and regularity estimates for symmetric nonlocal Dirichlet forms.
arXiv:1109.6812v2