• Harmonic Analysis and Operator Theory in Non-Standard Function Spaces
• Function spaces
• Potential type operators
• Hypersingular integrals
• Fractional Calculus

Rafeiro, H.; Rojas, E: “ Espacios de Lebesgue con Exponente Variable: Un espacio de Banach de funciones medibles” (in preparation)
Kokilashvili, V.; Meskhi, A.; Rafeiro, H.; Samko, S.: “Integral operators in nonstandard Banach function spaces” (submitted)

V. Kokilashvili, A. Meskhi, H. Rafeiro: “Grand Bochner-Lebesgue space and its associate space” (Journal of Functional Analysis)

Rafeiro, H.; Samko, N.; Samko, S. “Morrey-Campanato Spaces: an overview”, Operator eory: Advances and Applications, vol 228 Eds Y.I. Karlovich, L. Rodino, B. Silbermann, I.M. Spitkovsky, 293-323 Birkhäuser

Rafeiro, H. “A note on boundedness of operators in Grand Grand Morrey spaces”, Operator Theory: Advances and Applications, vol 229 Eds A. Almeida, L. Castro, F.-O. Speck, 349-356 Birkhäuser

Castillo, R.E.; Merentes, N.; Rafeiro, H. “Bounded variation spaces with p-variable”, Mediterr. J. Math.

Kokilashvili, V; Meskhi, A; Rafeiro, H. “Boundedness of commutators of singular and potential operators in gener- alized grand Morrey spaces and some applications”, Studia Math.

Kokilashvili, V; Meskhi, A; Rafeiro, H. “Estimates for nondivergence elliptic equations with VMO coefficients in generalized grand Morrey spaces”, Complex Var. Elliptic Equ.

Kokilashvili, V; Meskhi, A; Rafeiro, H. “Riesz type potential operators in generalized grand Morrey spaces”, Georgian Math. J., Vol.

Rafeiro, H.; Yakhshiboev, M., The Chen-Marchaud integro-differentiation in the variable exponent Lebesgue spaces. Fract. Calc. Appl. Anal., 14(3) (2011), 343--360.

Rafeiro, H., Samko, S. Variable exponent Campanato spaces , J. Math. Sciences, 172:1 (2011), 143-164 (russian version published in Problems in Mathematical Analysis 51, November 2010, 121-138)

Rafeiro, H.; Samko, S. Corrigendum to "Hardy type inequality in variable Lebesgue spaces". Ann. Acad. Sci. Fenn. Math. 35 (2010), no. 1, 679-680.

Rafeiro, H.; Samko, S. Characterization of the variable exponent Bessel potential spaces via the Poisson semigroup. J. Math. Anal. Appl. 365 (2010) 483-497.

Rafeiro, H. Kolmogorov compactness criterion in variable exponent Lebesgue spaces. Proc. A. Razmazde Math. Inst. 150 (2009), 105-113.

Rafeiro, H.; Samko, S. Hardy type inequality in variable Lebesgue spaces. Ann. Acad. Sci. Fenn. Math. 34 (2009), no. 1, 279-289.

Rafeiro, H.; Samko, S. Dominated compactness theorem in Banach function spaces and its applications. Complex Anal. Oper. Theory 2 (2008), no. 4, 669-681.

Rafeiro, H., Samko, S. Approximative method for the inversion of the Riesz potential operator in variable Lebesgue spaces. Fract. Calc. Appl. Anal. 11 (2008), no.3, 269-280.

Almeida, A.; Rafeiro, H. Inversion of the Bessel potential operator in weighted variable Lebesgue spaces. J. Math. Anal. Appl. 340 (2008), no. 2, 1336-1346.

Rafeiro, H.; Samko, S. Characterization of the range of one-dimensional fractional integration in the space with variable exponent, Operator Theory: Advances and Applications, vol 181, Eds M.A. Bastos, I. Gohberg, A.B. Lebre, (2008), 393-416, Birkhauser.

Rafeiro, H.; Samko, S. On a class of fractional type integral equations in variable exponent spaces. Fract. Calc. Appl. Anal. 10 (2007), no. 4, 399-421.

Rafeiro, H.; Samko, S. On multidimensional analogue of Marchaud formula for fractional Riesz-type derivatives in domains in Rn. Fract. Calc. Appl. Anal. 8 (2005), no. 4, 393-401.