Journal of Pure and Applied Mathematics: Advances and Applications[1] M. Abid, M. Slimane, I. Omrane and B. Halouani, Mixed wavelet
leaders multifractal formalism in a product of critical besov spaces,
Mediterranean Journal of Mathematics 14(4) (2017), 1-20; Article
176.
DOI: https://doi.org/10.1007/s00009-017-0964-0
[2] J. Aouidi and A. Ben Mabrouk, A wavelet multifractal formalism for
simultaneous singularities of functions, International Journal of
Wavelets, Multiresolution and Information Processing 12(1) (2014);
Article no. 1450009.
DOI: https://doi.org/10.1142/S021969131450009X
[3] L. Barreira, B. Saussol and J. Schmeling, Higher-dimensional
multifractal analysis, Journal de Mathématiques Pures et Appliquées
81(4) (2002), 67-91.
DOI: https://doi.org/10.1016/S0021-7824(01)01228-4
[4] L. Barreira and P. Doutor, Birkhoff averages for hyperbolic flows:
Variational principles and applications, Journal of Statistical
Physics 115(5-6) (2004), 1567-1603.
DOI: https://doi.org/10.1023/B:JOSS.0000028069.64945.65
[5] L. Barreira and P. Doutor, Almost additive multifractal analysis,
Journal de Mathématiques Pures et Appliquées 92(1) (2009), 1-17.
DOI: https://doi.org/10.1016/j.matpur.2009.04.006
[6] L. Barreira and P. Doutor, Dimension spectra of almost additive
sequences, Nonlinearity 22(11) (2009), 2761-2773.
DOI: https://doi.org/10.1088/0951-7715/22/11/009
[7] L. Barreira, Y. Cao and J. Wang, Multifractal analysis of
asymptotically additive sequences, Journal of Statistical Physics
153(5) (2013), 888-910.
DOI: https://doi.org/10.1007/s10955-013-0853-2
[8] J. Barral and I. Bhouri, Multifractal analysis for projections of
Gibbs and related measures, Ergodic Theory and Dynamic Systems 31(3)
(2011), 673-701.
DOI: https://doi.org/10.1017/S0143385710000143
[9] M. Ben Slimane, Baire typical results for mixed Hölder spectra on
product of continuous Besov or oscillation spaces, Mediterranean
Journal of Mathematics 13(4) (2016), 1513-1533.
DOI: https://doi.org/10.1007/s00009-015-0592-5
[10] M. Ben Slimane, A. Ben Mabrouk and Jamil Aouidi, Mixed
multifractal analysis for functions: General upper bound and optimal
results for vectors of self-similar or quasi-self-similar of functions
and their superpositions, Fractals 24(4) (2016); Article 1650039.
DOI: https://doi.org/10.1142/S0218348X16500390
[11] J. Cole, Relative multifractal analysis, Chaos, Solitons &
Fractals 11(14) (2000), 2233-2250.
DOI: https://doi.org/10.1016/S0960-0779(99)00143-5
[12] M. Dai, Mixed self-conformal multifractal measures, Analysis in
Theory and Applications 25(2) (2009), 154-165.
DOI: https://doi.org/10.1007/s10496-009-0154-4
[13] M. Dai and Y. Shi, Typical behavior of mixed 
Nonlinear Analysis: Theory, Methods &
Applications 72(5) (2010), 2318-2325.
DOI: https://doi.org/10.1016/j.na.2009.10.032
[14] M. Dai and W. Li, The mixed 
of self-conformal measures satisfying the weak
separation condition, Journal of Mathematical Analysis and
Applications 382(1) (2011), 140-147.
DOI: https://doi.org/10.1016/j.jmaa.2011.04.037
[15] C. Wang, H. Sun and M. Dai, Mixed generalized dimensions of
random self-similar measures, International Journal of Nonlinear
Science 13(1) (2012), 123-128.
[16] M. Dai, J. Hou, J. Gao, W. Su, L. Xi and D. Ye, Mixed
multifractal analysis of China and US stock index series, Chaos,
Solitons & Fractals 87 (2016), 268-275.
DOI: https://doi.org/10.1016/j.chaos.2016.04.013
[17] M. Dai, S. Shao, J. Gao, Y. Sun and W. Su, Mixed multifractal
analysis of crude oil, gold and exchange rate series, Fractals 24(1)
(2016); Article 1650046.
DOI: https://doi.org/10.1142/S0218348X16500468
[18] Z. Douzi and B. Selmi, Multifractal variation for projections of
measures, Chaos, Solitons & Fractals 91 (2016), 414-420.
DOI: https://doi.org/10.1016/j.chaos.2016.06.026
[19] Z. Douzi and B. Selmi, On the Projections of Mutual Multifractal
Spectra, arXiv: 1805.06866v1, 2018.
[20] Z. Douzi and B. Selmi, On the projections of the mutual
multifractal Rényi dimensions, Analysis in Theory and Applications
(to appear).
[21] K. J. Falconer and J. D. Howroyd, Packing dimensions of
projections and dimensions profiles, Mathematical Proceedings of the
Cambridge Philosophical Society 121(2) (1997), 269-286.
DOI: https://doi.org/10.1017/S0305004196001375
[22] K. J. Falconer and P. Mattila, The packing dimensions of
projections and sections of measures, Mathematical Proceedings of the
Cambridge Philosophical Society 119(4) (1996), 695-713.
DOI: https://doi.org/10.1017/S0305004100074533
[23] K. J. Falconer and T. C. O’Neil, Convolutions and the geometry
of multifractal measures, Mathematische Nachrichten 204(1) (1999),
61-82.
DOI: https://doi.org/10.1002/mana.19992040105
[24] O. Frostman, Potential d’Équilibre et capacité des ensembles
avec quelques applications á la théorie des functions, Meddel Lunds
University Math. Sem. 3 (1935), 1-118.
[25] B. R. Hunt and V. Y. Kaloshin, How projections affect the
dimension spectrum of fractal measures, Nonlinearity 10(5) (1997),
1031-1046.
DOI: https://doi.org/10.1088/0951-7715/10/5/002
[26] X. Hu and S. J. Taylor, Fractal properties of products and
projections of measures in 
Mathematical Proceedings of the Cambridge
Philosophical Society 115(3) (1994), 527-544.
DOI: https://doi.org/10.1017/S0305004100072285
[27] E. Järvenpää, M. Järvenpää, F. Ledrappier and M. Leikas,
One-dimensional families of projections, Nonlinearity 21(3) (2008),
453-464.
DOI: https://doi.org/10.1088/0951-7715/21/3/005
[28] E. Järvenpää, M. Järvenpää and T. Keleti, Hausdorff
dimension and non-degenerate families of projections, The Journal of
Geometric Analysis 24(4) (2014), 2020-2034.
DOI: https://doi.org/10.1007/s12220-013-9407-8
[29] R. Kaufman, On Hausdorff dimension of projections, Mathematika
15(2) (1968), 153-155.
DOI: https://doi.org/10.1112/S0025579300002503
[30] J. M. Marstrand, Some fundamental geometrical properties of plane
sets of fractional dimensions, Proceedings of the London Mathematical
Society 4(1) (1954), 257-302.
DOI: https://doi.org/10.1112/plms/s3-4.1.257
[31] P. Mattila, The Geometry of Sets and Measures in Euclidean
Spaces, Cambridge University Press, Cambridge, 1995.
[32] M. Menceur, A. Ben Mabrouk and K. Betina, The multifractal
formalism for measures, review and extension to mixed cases, Analysis
in Theory and Applications 32(4) (2016), 303-332.
DOI: https://doi.org/10.4208/ata.2016.v32.n4.1
[33] J. Li, L. Olsen and M. Wu, Bounds for the of self-similar measures without any separation
conditions, Journal of Mathematical Analysis and Applications 387(1)
(2012), 77-89.
DOI: https://doi.org/10.1016/j.jmaa.2011.08.065
[34] T. C. O’Neil, The multifractal spectra of projected measures in
Euclidean spaces, Chaos, Solitons & Fractals 11(6) (2000), 901-921.
DOI: https://doi.org/10.1016/S0960-0779(98)00256-2
[35] L. Olsen, A multifractal formalism, Advances in Mathematics 116
(1995), 82-196.
DOI: https://doi.org/10.1006/aima.1995.1066
[36] L. Olsen, Mixed generalized dimensions of self-similar measures,
Journal of Mathematical Analysis and Applications 306(2) (2005),
516-539.
DOI: https://doi.org/10.1016/j.jmaa.2004.12.022
[37] L. Olsen, Bounds for the of a self-similar multifractal not satisfying
the open set condition, Journal of Mathematical Analysis and
Applications 355(1) (2009), 12-21.
DOI: https://doi.org/10.1016/j.jmaa.2009.01.037
[38] L. Olsen, On the inverse multifractal formalism, Glasgow
Mathematical Journal 52(1) (2010), 179-194.
DOI: https://doi.org/10.1017/S0017089509990279
[39] B. Selmi, A note on the effect of projections on both measures
and the generalization of q-dimension capacity, Problemy
Analiza-Issues of Analysis 5(2) (2016), 38-51.
DOI: https://doi.org/10.15393/j3.art.2016.3290
[40] B. Selmi, Measure of relative multifractal exact dimensions,
Advances and Applications in Mathematical Sciences 17(10) (2018),
629-643.
[41] B. Selmi, Multifractal dimensions for projections of measures,
Boletim da Sociedade Paranaense de Matemática (to appear).
[42] B. Selmi, On the strong regularity with the multifractal measures
in a probability space, Analysis and Mathematical Physics 9(3) (2019),
1525-1534.
DOI: https://doi.org/10.1007/s13324-018-0261-5
[43] B. Selmi, On the effect of projections on the Billingsley
dimensions, Asian-European Journal of Mathematics 13 (2020),
2050128/1-17.
DOI: https://doi.org/10.1142/S1793557120501284
[44] B. Selmi, On the projections of the multifractal packing
dimension for 
Annali di Matematica Pura ed Applicata (to
appear).
DOI: https://doi.org/10.1007/s10231-019-00929-7
[45] B. Selmi and N. Yu. Svetova, On the projections of mutual
Problemy Analiza-Issues of Analysis 6(1)
(2017), 94-108.
DOI: https://doi.org/10.15393/j3.art.2017.4231
[46] N. Yu. Svetova, Mutual multifractal spectra II: Legendre and
Hentschel-Procaccia spectra, and spectra defined for partitions, Tr.
Petrozavodsk. Gos. Univ. Ser. Mat. 11 (2004), 47-56.
[47] N. Yu. Svetova, The property of convexity of mutual multifractal
dimension, Tr. Petrozavodsk. Gos. Univ. Ser. Mat. 17 (2010), 15-24.
[48] N. Yu. Svetova, Mutual multifractal spectra I: Exact spectra, Tr.
Petrozavodsk. Gos. Univ. Ser. Mat. 11 (2004), 41-46.
[49] N. Yu. Svetova, An estimate for exact mutual multifractal
spectra, Tr. Petrozavodsk. Gos. Univ. Ser. Mat. 14 (2008), 59-66.
