Let
be an orthonormal basis of the Euclidean space
.

The complex Clifford algebra, denoted by
, is generated additively by elements of the form

where
is such that
, and so the complex dimension of
is
. For
,
is the identity element.

For
, the conjugation and the main involution are defined, respectively, as

If we identify the vectors
of
with the real Clifford vectors
, then
may be considered as a subspace of
.

The product of two Clifford vectors splits up into two parts:

where

Generally speaking, we will consider
-valued functions
on
of the form

where
are
-valued functions. Notions of continuity and differentiability of
are introduced by means of the corresponding notions for its complex components
.

In particular, for bounded set
, the class of continuous functions which satisfy the Hölder condition of order
in
will be denoted by
.

Let us introduce the so-called Dirac operator given by

It is a first-order elliptic operator whose fundamental solution is given by

where
is the area of the unit sphere in
.

If
is open in
and
, then
is said to be monogenic if
in
. Denote by
the set of all monogenic functions in
. The best general reference here is [9].

We recall (see [10]) that a Whitney extension of
,
being compact in
, is a compactly supported function
such that
and

Here and in the sequel, we will denote by
certain generic positive constant not necessarily the same in different occurrences.

The following assumption will be needed through the paper. Let
be a Jordan domain, that is, a bounded oriented connected open subset of
whose boundary
is a compact topological surface. By
we denote the complement domain of
.

By definition (see [11]) the box dimension of
, denoted by
, is equal to
where
stands for the least number of
-balls needed to cover
.

The limit above is unchanged if
is thinking as the number of
-cubes with
intersecting
. A cube
is called a
-cube if it is of the form:
where
are integers.

Fix
, assuming that the improper integral
converges. Note that this is in agreement with [12] for
to be
-summable.

Observe that a
-summable surface has box dimension
. Meanwhile, if
has box dimension less than
, then
is
-summable.